Question

find the value of n so that (-5)n+2 ×(-5)3=(-5)7​

Answer 1

I think so 13 will be the answer.

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $(-5)^{n+2}\times (-5)^3 = (-5)^7$

To Find:

• Value of n

Solution:

$\implies (-5)^{n+2}\times (-5)^3 = (-5)^7 \\ \implies (-5)^{n+2+3} = (-5)^7 \\ \implies (-5)^{n+5} = (-5)^7 \\ As\;the\;bases\;are\;same,\;we\;compare\;the\;powers,\\ \implies n+5 = 7 \\ \implies n = 7-5 \\ \bold{\implies n = 2}$

Formula Used:

• $a^m * a^n = a^{m+n}$

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$