3.7: Negative Exponents (2024)

Reciprocals

Two real numbers are said to be reciprocals of each other if their product is 1. Every nonzero real number has exactly one reciprocal, as shown in the examples below. Zero has no reciprocal.

Example \(\PageIndex{1}\)

\(4 \cdot \dfrac{1}{4} = 1\). This means that \(4\) and \(\dfrac{1}{4}\) are reciprocals.

Example \(\PageIndex{2}\)

\(6 \cdot \dfrac{1}{6} = 1\). This means that \(6\) and \(\dfrac{1}{6}\) are reciprocals.

Example \(\PageIndex{3}\)

\(-2 \cdot \dfrac{-1}{2} = 1\). This means that \(-2\) and \(-\dfrac{1}{2}\) are reciprocals.

Example \(\PageIndex{4}\)

\(a \cdot \dfrac{1}{a} = 1\). This means that \(a\) and \(\dfrac{1}{a}\) are reciprocals.

Example \(\PageIndex{5}\)

\(x \cdot \dfrac{1}{x} = 1\). This means that \(x\) and \(\dfrac{1}{x}\) are reciprocals.

Example \(\PageIndex{6}\)

\(x^3 \cdot \dfrac{1}{x^3} = 1\). This means that \(x^3\) and \(\dfrac{1}{x^3}\) are reciprocals.

Negative Exponent Definition

If \(n\) is any natural number and \(x\) is any nonzero real number, then:

\(x^{-n} = \dfrac{1}{x^n}\)

Example \(\PageIndex{7}\)

\(x^{-6} = \dfrac{1}{x^6}\)

Example \(\PageIndex{8}\)

\(a^{-1} = \dfrac{1}{a^a} = \dfrac{1}{a}\)

Example \(\PageIndex{9}\)

\(7^{-2} = \dfrac{1}{7^2} = \dfrac{1}{49}\)

Example \(\PageIndex{10}\)

\((3a)^{-6} = \dfrac{1}{(3a)^6}\)

Example \(\PageIndex{11}\)

\((5x-1)^{-24} = \dfrac{1}{(5x-1)^{-24}}\)

Example \(\PageIndex{12}\)

\((k+2x)^{-(-8)} = (k+2z)^8\)

Practice Problem \(\PageIndex{1}\)

\(y^{-5}\)

Answer

\(\dfrac{1}{y^5}\)

Practice Problem \(\PageIndex{2}\)

\(m^{-2}\)

Answer

\(\dfrac{1}{m^2}\)

Practice Problem \(\PageIndex{3}\)

\(3^{-2}\)

Answer

\(\dfrac{1}{9}\)

Practice Problem \(\PageIndex{4}\)

\(5^{-1}\)

Answer

\(\dfrac{1}{5}\)

Practice Problem \(\PageIndex{5}\)

\(2^{-4}\)

Answer

\(\dfrac{1}{16}\)

Practice Problem \(\PageIndex{6}\)

\((xy)^{-4}\)

Answer

\(\dfrac{1}{(xy)^4}\)

Practice Problem \(\PageIndex{7}\)

\((a+2b)^{-12}\)

Answer

\(\dfrac{1}{(a+2b)^{12}}\)

Practice Problem \(\PageIndex{8}\)

\((m-n)^{-(-4)}\)

Answer

\((m-n)^4\)

Note

It is important to note that \(a^{-n}\) is not necessarily a negative number. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9}\) \(3^{-2} \not = \ -9\)

Moving Factors Up and Down

In a fraction, a factor can be moved from the numerator to the denominator or from the denominator to the numerator by changing the sign of the exponent.

Example \(\PageIndex{13}\)

\(x^{-2}y^5\).

The factor \(x^{-2}\) can be moved from the numerator to the denominator by changing the exponent \(-2\) to \(+2\)

\(x^{-2}y^5 = \dfrac{y^5}{x^2}\)

Example \(\PageIndex{14}\)

\(a^9b^{-3}\).

The factor \(b^{-3}\) can be moved from the numerator to the denominator by changing the exponent \(-3\) to \(+3\).

\(a^9b^{-3} = \dfrac{a^9}{b^3}\)

Example \(\PageIndex{15}\)

\(\dfrac{a^4b^2}{c^{-6}}\).

This fraction can be written without any negative exponents by moving the factor \(c^{-6}\) into the numerator.
We must change the \(-6\) to \(+6\) to make the move legitimate.

\(\dfrac{a^4b^2}{c^{-6}} = a^4b^2c^6\)

Example \(\PageIndex{16}\)

\(\dfrac{1}{x^{-3}y^{-2}z^{-1}}\).

This fraction can be written without negative exponents by moving all the factors from the denominator to the numerator. Change the sign of each exponent: \(-3\) to \(+3\), \(-2\) to \(+2\), \(-1\) to \(+1\).

\(\dfrac{1}{x^{-3}y^{-2}z^{-1}} = x^3y^2z^1 = x^3y^2z\)

Practice Problem \(\PageIndex{9}\)

\(x^{-4}y^7\)

Answer

\(\dfrac{y^7}{x^4}\)

Practice Problem \(\PageIndex{10}\)

\(\dfrac{a^2}{b^{-4}}\)

Answer

\(a^2b^4\)

Practice Problem \(\PageIndex{11}\)

\(\dfrac{x^3y^4}{z^{-8}}\)

Answer

\(x^3y^4z^8\)

Practice Problem \(\PageIndex{12}\)

\(\dfrac{6m^{-3}n^{-2}}{7k^{-1}}\)

Answer

\(\dfrac{6k}{7m^3n^2}\)

Practice Problem \(\PageIndex{13}\)

\(\dfrac{1}{a^{-2}b^{-6}c^{-8}}\)

Answer

\(a^2b^6c^8\)

Practice Problem \(\PageIndex{14}\)

\(\dfrac{3a(a-5b)^{-2}}{5b(a-4b)^5}\)

Answer

\(\dfrac{3a}{5b(a-5b)^2(a-4b)^5}\)

Example \(\PageIndex{17}\)

Rewrite \(\dfrac{24 a^{7} b^{9}}{2^{3} a^{4} b^{-6}}\) in a simpler form.
Notice that we are dividing powers with the same base. We'll proceed by using the rules of exponents.
\(
\begin{aligned}
\dfrac{24 a^{7} b^{9}}{2^{3} a^{4} b^{-6}}=\dfrac{24 a^{7} b^{9}}{8 a^{4} b^{-6}} &=3 a^{7-4} b^{9-(-6)} \\
&=3 a^{3} b^{9+6} \\
&=3 a^{3} b^{15}
\end{aligned}
\)

Example \(\PageIndex{17}\)

Write \(\dfrac{9 a^{5} b^{3}}{5 x^{3} y^{2}}\) so that no denominator appears.
We can eliminate the denominator by moving all factors that make up the denominator to the numerator.
\(9 a^{5} b^{3} 5^{-1} x^{-3} y^{-2}\)

Example \(\PageIndex{17}\)

Find the value of \(\dfrac{1}{10^{-2}}+\dfrac{3}{4^{-3}}\)
We can evaluate this expression by eliminating the negative exponents.
\(
\begin{aligned}
\dfrac{1}{10^{-2}}+\dfrac{3}{4^{-3}} &=1 \cdot 10^{2}+3 \cdot 4^{3} \\
&=1 \cdot 100+3 \cdot 64 \\
&=100+192 \\
&=292
\end{aligned}
\)

Practice Problem \(\PageIndex{15}\)

Rewrite \(\dfrac{36x^8b^3}{3^2x^{-2}b^{-5}}\) in a simpler form.

Answer

\(4x^{10}b^8\)

Practice Problem \(\PageIndex{16}\)

Write \(\dfrac{2^4m^{-3}n^7}{4^{-1}x^5}\) in a simpler form and one in which no denominator appears.

Answer

\(64m^{-3}n^7x^{-5}\)

Practice Problem \(\PageIndex{17}\)

Find the value of \(\dfrac{2}{5^{-2}} + 6^{-2} \cdot 2^3 \cdot 3^2\)

Answer

\(52\)

Exercise \(\PageIndex{1}\)

\(x^{-2}\)

Answer

\(\dfrac{1}{x^{-2}}\)

Exercise \(\PageIndex{2}\)

\(x^{-4}\)

Exercise \(\PageIndex{3}\)

\(x^{-7}\)

Answer

\(\dfrac{1}{x^7}\)

Exercise \(\PageIndex{4}\)

\(a^{-8}\)

Exercise \(\PageIndex{5}\)

\(a^{-10}\)

Answer

\(\dfrac{1}{a^{-10}}\)

Exercise \(\PageIndex{6}\)

\(b^{-12}\)

Exercise \(\PageIndex{7}\)

\(b^{-14}\)

Answer

\(\dfrac{1}{b^{14}}\)

Exercise \(\PageIndex{8}\)

\(y^{-1}\)

Exercise \(\PageIndex{9}\)

\(y^{-5}\)

Answer

\(\dfrac{1}{y^5}\)

Exercise \(\PageIndex{10}\)

\((x+1)^{-2}\)

Exercise \(\PageIndex{11}\)

\((x-5)^{-3}\)

Answer

\(\dfrac{1}{(x-5)^3}\)

Exercise \(\PageIndex{12}\)

\((y-4)^{-6}\)

Exercise \(\PageIndex{13}\)

\((a+9)^{-10}\)

Answer

\(\dfrac{1}{(a+9)^{10}}\)

Exercise \(\PageIndex{14}\)

\((r+3)^{-8}\)

Exercise \(\PageIndex{15}\)

\((a-1)^{-12}\)

Answer

\(\dfrac{1}{(a-1)^{12}}\)

Exercise \(\PageIndex{16}\)

\(x^3y^{-2}\)

Exercise \(\PageIndex{17}\)

\(x^7y^{-5}\)

Answer

\(\dfrac{x^7}{y^5}\)

Exercise \(\PageIndex{18}\)

\(a^4b^{-1}\)

Exercise \(\PageIndex{19}\)

\(a^7b^{-8}\)

Answer

\(\dfrac{a^7}{b^8}\)

Exercise \(\PageIndex{20}\)

\(a^2b^3c^{-2}\)

Exercise \(\PageIndex{21}\)

\(x^3y^2z^{-6}\)

Answer

\(\dfrac{x^3y^2}{z^6}\)

Exercise \(\PageIndex{22}\)

\(x^3y^{-4}z^2w\)

Exercise \(\PageIndex{23}\)

\(a^7b^{-9}zw^3\)

Answer

\(\dfrac{a^7zw^3}{b^9}\)

Exercise \(\PageIndex{24}\)

\(a^3b^{-1}zw^2\)

Exercise \(\PageIndex{25}\)

\(x^5y^{-5}z^{-2}\)

Answer

\(\dfrac{x^5}{y^5z^2}\)

Exercise \(\PageIndex{26}\)

\(x^4y^{-8}z^{-3}w^{-4}\)

Exercise \(\PageIndex{27}\)

\(a^{-4}b^{-6}c^{-1}d^4\)

Answer

\(\dfrac{d^4}{a^4b^6c}\)

Exercise \(\PageIndex{28}\)

\(x^9y^{-6}z^{-1}w^{-5}r^{-2}\)

Exercise \(\PageIndex{29}\)

\(4x^{-6}y^2\)

Answer

\(\dfrac{4y^2}{x^6}\)

Exercise \(\PageIndex{30}\)

\(5x^2y^2z^{-5}\)

Exercise \(\PageIndex{31}\)

\(7a^{-2}b^2c^2\)

Answer

\(\dfrac{7b^2c^2}{a^2}\)

Exercise \(\PageIndex{32}\)

\(4x^3(x+1)^2y^{-4}z^{-1}\)

Exercise \(\PageIndex{33}\)

\(7a^2(a-4)^3b^{-6}c^{-7}\)

Answer

\(\dfrac{7a^2(a-4)^3}{b^6c^7}\)

Exercise \(\PageIndex{34}\)

\(18b^{-6}(b^2-3)^{-5}c^{-4}d^5e^{-1}\)

Exercise \(\PageIndex{35}\)

\(7(w+2)^{-2}(w+1)^3\)

Answer

\(\dfrac{7(w+1)^3}{(w+2)^2}\)

Exercise \(\PageIndex{36}\)

\(2(a-8)^{-3}(a-2)^5\)

Exercise \(\PageIndex{37}\)

\((x^2+3)^3(x^2-1)^{-4}\)

Answer

\(\dfrac{(x^2+3)^3}{(x^2-1)^4}\)

Exercise \(\PageIndex{38}\)

\((x^4+2x-1)^{-6}(x+5)^4\)

Exercise \(\PageIndex{39}\)

\((3x^2-4x-8)^{-9}(2x+11)^{-3}\)

Answer

\(\dfrac{1}{(3x^2-4x-8)^{9}(2x+11)^{3}}\)

Exercise \(\PageIndex{40}\)

\((5y^2+8y-6)^{-2}(6y-1)^{-7}\)

Exercise \(\PageIndex{41}\)

\(7a(a^2-4)^{-2}(b^2-1)^{-2}\)

Answer

\(\dfrac{7a}{(a^2-4)^2(b^2-1)^2}\)

Exercise \(\PageIndex{42}\)

\((x-5)^{-4}3b^2c^4(x+6)^8\)

Exercise \(\PageIndex{43}\)

\((y^3+1)^{-1}5y^3z^{-4}w^{-2}(y^3-1)^{-2}\)

Answer

\(\dfrac{5y^3}{(y^3+1)z^4w^2(y^3-1)^2}\)

Exercise \(\PageIndex{44}\)

\(5x^3(2x^{-7})\)

Exercise \(\PageIndex{45}\)

\(3y^{-3}(9x)\)

Answer

\(\dfrac{27x}{y^3}\)

Exercise \(\PageIndex{46}\)

\(6a^{-4}(2a^{-6})\)

Exercise \(\PageIndex{47}\)

\(4a^2b^2a^{-5}b^{-2}\)

Answer

\(\dfrac{4}{a^3}\)

Exercise \(\PageIndex{48}\)

\(5^{-1}a^{-2}b^{-6}b^{-11}c^{-3}c^9\)

Exercise \(\PageIndex{49}\)

\(2^3x^22^{-3}x^{-2}\)

Answer

\(1\)

Exercise \(\PageIndex{50}\)

\(7a^{-3}b^{-9} \cdot 5a^6bc^{-2}c^4\)

Exercise \(\PageIndex{51}\)

\((x+5)^2(x+5)^{-6}\)

Answer

\(\dfrac{1}{(x+5)^4}\)

Exercise \(\PageIndex{52}\)

\((a-4)^3(a-4)^{-10}\)

Exercise \(\PageIndex{53}\)

\(8(b+2)^{-8}(b+2)^{-4}(b+2)^3\)

Answer

\(\dfrac{8}{(b+2)^9}\)

Exercise \(\PageIndex{54}\)

\(3a^5b^{-7}(a^2+4)^{-3}6a^{-4}b(a^2+4)^{-1}(a^2+4)\)

Exercise \(\PageIndex{55}\)

\(-4a^3b^{-5}(2a^2b^7c^{-2})\)

Answer

\(\dfrac{-8a^5b^2}{c^2}\)

Exercise \(\PageIndex{56}\)

\(-2x^{-2}y^{-4}z^4(-6x^3y^{-3}z)\)

Exercise \(\PageIndex{57}\)

\((-5)^2(-5)^{-1}\)

Answer

\(-5\)

Exercise \(\PageIndex{58}\)

\((-9)^{-3}(9)^3\)

Exercise \(\PageIndex{59}\)

\((-1)^{-1}(-1)^{-1}\)

Answer

\(1\)

Exercise \(\PageIndex{60}\)

\((4)^2(2)^{-4}\)

Exercise \(\PageIndex{61}\)

\(\dfrac{1}{a^{-4}}\)

Answer

\(a^4\)

Exercise \(\PageIndex{62}\)

\(\dfrac{1}{a^{-1}}\)

Exercise \(\PageIndex{63}\)

\(\dfrac{4}{x^{-6}}\)

Answer

\(4x^6\)

Exercise \(\PageIndex{64}\)

\(\dfrac{7}{x^{-8}}\)

Exercise \(\PageIndex{65}\)

\(\dfrac{23}{y^{-1}}\)

Answer

\(23y\)

Exercise \(\PageIndex{66}\)

\(\dfrac{6}{a^2b^{-4}}\)

Exercise \(\PageIndex{67}\)

\(\dfrac{3c^5}{a^3b^{-3}}\)

Answer

\(\dfrac{3b^3c^5}{a^3}\)

Exercise \(\PageIndex{68}\)

\(\dfrac{16a^{-2}b^{-6}c}{2yz^{-5}w^{-4}}\)

Exercise \(\PageIndex{69}\)

\(\dfrac{24y^2z^{-8}}{6a^2b^{-1}c^{-9}d^3}\)

Answer

\(\dfrac{4bc^9y^2}{a^2d^3z^8}\)

Exercise \(\PageIndex{70}\)

\(\dfrac{3^{-1}b^5(b+7)^{-4}}{9^{-1}a^{-4}(a+7)^2}\)

Exercise \(\PageIndex{71}\)

\(\dfrac{36a^6b^5c^8}{3^2a^3b^7c^9}\)

Answer

\(\dfrac{4a^3}{b^2c}\)

Exercise \(\PageIndex{72}\)

\(\dfrac{45a^4b^2c^6}{15a^2b^7c^8}\)

Exercise \(\PageIndex{73}\)

\(\dfrac{3^3x^4y^3z}{3^2xy^5z^5}\)

Answer

\(\dfrac{3x^3}{y^2z^4}\)

Exercise \(\PageIndex{74}\)

\(\dfrac{21x^2y^2z^5w^4}{7xyz^{12}w^{14}}\)

Exercise \(\PageIndex{75}\)

\(\dfrac{33a^{-4}b^{-7}}{11a^3b^{-2}}\)

Answer

\(\dfrac{3}{a^7b^5}\)

Exercise \(\PageIndex{76}\)

\(\dfrac{51x^{-5}y^{-3}}{3xy}\)

Exercise \(\PageIndex{77}\)

\(\dfrac{2^6x^{-5}y^{-2}a^{-7}b^5}{2^{-1}x^{-4}y^{-2}b^6}\)

Answer

\(\dfrac{128}{a^7bx}\)

Exercise \(\PageIndex{78}\)

\(\dfrac{(x+3)^3(y-6)^4}{(x+3)^5(y-6)^{-8}}\)

Exercise \(\PageIndex{79}\)

\(\dfrac{4x^3}{y^7}\)

Answer

\(\dfrac{4x^3}{y^7}\)

Exercise \(\PageIndex{80}\)

\(\dfrac{5x^4y^3}{a^3}\)

Exercise \(\PageIndex{81}\)

\(\dfrac{23a^4b^5c^{-2}}{x^{-6}y^5}\)

Answer

\(\dfrac{23a^4b^5x^6}{c^2y^5}\)

Exercise \(\PageIndex{82}\)

\(\dfrac{2^3b^5c^2d^{-9}}{4b^4cx}\)

Exercise \(\PageIndex{83}\)

\(\dfrac{10x^3y^{-7}}{3x^5z^2}\)

Answer

\(\dfrac{10}{3x^2y^7z^2}\)

Exercise \(\PageIndex{84}\)

\(\dfrac{3x^2y^{-2}(x-5)}{9^{-1}(x+5)^3}\)

Exercise \(\PageIndex{85}\)

\(\dfrac{14a^2b^2c^{-12}(a^2+21)^{-4}}{4^{-2}a^2b^{-1}(a+6)^3}\)

Answer

\(\dfrac{224b^3}{c^{12}(a^2+21)^4(a+6)^3}\)

Exercise \(\PageIndex{86}\)

\(4^{-1}\)

Exercise \(\PageIndex{87}\)

\(7^{-1}\)

Answer

\(\dfrac{1}{7}\)

Exercise \(\PageIndex{88}\)

\(6^{-2}\)

Exercise \(\PageIndex{89}\)

\(2^{-5}\)

Answer

\(\dfrac{1}{32}\)

Exercise \(\PageIndex{90}\)

\(3^{-4}\)

Exercise \(\PageIndex{91}\)

\(6 \cdot 3^{-3}\)

Answer

\(\dfrac{2}{9}\)

Exercise \(\PageIndex{92}\)

\(4 \cdot 9^{-2}\)

Exercise \(\PageIndex{93}\)

\(28 \cdot 14^{-1}\)

Answer

\(2\)

Exercise \(\PageIndex{94}\)

\(2^{-3}(3^{-2})\)

Exercise \(\PageIndex{95}\)

\(2^{-1} \cdot 3^{-1} \cdot 4^{-1}\)

Answer

\(\dfrac{1}{24}\)

Exercise \(\PageIndex{96}\)

\(10^{-2} + 3(10^{-2})\)

Exercise \(\PageIndex{97}\)

\((-3)^{-2}\)

Answer

\(\dfrac{1}{9}\)

Exercise \(\PageIndex{98}\)

\((-10)^{-1}\)

Exercise \(\PageIndex{99}\)

\(\dfrac{3}{2^{-3}}\)

Answer

\(24\)

Exercise \(\PageIndex{100}\)

\(\dfrac{4^{-1}}{5^{-2}}\)

Exercise \(\PageIndex{101}\)

\(\dfrac{2^4-7}{4^{-1}}\)

Answer

\(36\)

Exercise \(\PageIndex{102}\)

\(\dfrac{2^{-1}+4^{-1}}{2^{-2} + 4^{-2}}\)

Exercise \(\PageIndex{103}\)

\(\dfrac{21^0-2^6}{2 \cdot 6-13}\)

Answer

\(63\)

Exercise \(\PageIndex{104}\)

\((a^6)^{-2}\)

Exercise \(\PageIndex{105}\)

\((a^5)^{-3}\)

Answer

\(\dfrac{1}{a^{15}}\)

Exercise \(\PageIndex{106}\)

\((x^7)^{-4}\)

Exercise \(\PageIndex{107}\)

\((x^4)^{-8}\)

Answer

\(\dfrac{1}{x^{32}}\)

Exercise \(\PageIndex{108}\)

\((b^{-2})^7\)

Exercise \(\PageIndex{109}\)

\((b^{-4})^{-1}\)

Answer

\(b^4\)

Exercise \(\PageIndex{110}\)

\((y^{-3})^{-4}\)

Exercise \(\PageIndex{111}\)

\((y^{-9})^{-3}\)

Answer

\(y^{27}\)

Exercise \(\PageIndex{112}\)

\((a^{-1})^{-1}\)

Exercise \(\PageIndex{113}\)

\((b^{-1})^{-1}\)

Answer

\(b\)

Exercise \(\PageIndex{114}\)

\((a^0)^{-1}\), \(a \not = 0\)

Exercise \(\PageIndex{115}\)

\((m^))^{-1}\), \(m \not = 0\)

Answer

\(1\)

Exercise \(\PageIndex{116}\)

\((x^{-3}y^7)^{-4}\)

Exercise \(\PageIndex{117}\)

\((x^6y^6z^{-1})^2\)

Answer

\(\dfrac{x^{12}y^{12}}{z^2}\)

Exercise \(\PageIndex{118}\)

\((a^{-5}b^{-1}c^0)^6\)

Exercise \(\PageIndex{119}\)

\((\dfrac{y^3}{x^{-4}})^5\)

Answer

\(x^{20}y^{15}\)

Exercise \(\PageIndex{120}\)

\((\dfrac{a^{-8}}{b^{-6}})^3\)

Exercise \(\PageIndex{121}\)

\((\dfrac{2a}{b^3})^4\)

Answer

\(\dfrac{16a^4}{b^{12}}\)

Exercise \(\PageIndex{122}\)

\((\dfrac{3b}{a^2})^{-5}\)

Exercise \(\PageIndex{123}\)

\((\dfrac{5^{-1}a^3b^{-6}}{x^{-2}y^9})^2\)

Answer

\(\dfrac{a^6x^4}{25b^{12}y^{18}}\)

Exercise \(\PageIndex{124}\)

\((\dfrac{4m^{-3}n^6}{2m^{-5}n})^3\)

Exercise \(\PageIndex{125}\)

\((\dfrac{r^5s^{-4}}{m^{-8}n^7})^{-4}\)

Answer

\(\dfrac{n^{28}s^{16}}{m^{32}r^{20}}\)

Exercise \(\PageIndex{126}\)

\((\dfrac{h^{-2}j^{-6}}{k^{-4}p})^{-5}\)

Exercise \(\PageIndex{127}\)

Simplify \((4x^5y^3z^0)^3\)

Answer

\(64x^{15}y^9\)

Exercise \(\PageIndex{128}\)

Find the sum. \(-15 + 3\)

Exercise \(\PageIndex{129}\)

Find the difference. \(8 -(-12)\)

Answer

\(20\)

Exercise \(\PageIndex{130}\)

Simplify \((-3)(-8) + 4(-5)\)

Exercise \(\PageIndex{131}\)

Find the value of \(m\) if \(m = \dfrac{-3k-5t}{kt+6}\) when \(k = 4\) and \(t = -2\)

Answer

\(1\)