Question

find m so the (-5)m+2 x (-5)^6=(-5)^10​

Answer 1

Given Question :-

Solve for m :-

$\tt \: {( - 5)}^{m + 2} \times {( - 5)}^{6} = {( - 5)}^{10}$

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used \::}}}} \end{gathered}$

Laws of exponents

$\begin{gathered}(1)\:{\underline{\boxed{\bf{{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(2)\:{\underline{\boxed{\bf{{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(3)\:{\underline{\boxed{\bf{{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(4)\:{\underline{\boxed{\bf{ {(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(5)\:{\underline{\boxed{\bf{{ {x}^{0} = 1}}}}} \\ \end{gathered}$

$\begin{gathered}(6)\:{\underline{\boxed{\bf{if \: { {x}^{m} = {x}^{n} \: then \: m \: = \: n}}}}} \\ \end{gathered}$

$\large\underline{\bold{Solution - }}$

$\rm :\longmapsto\: {( - 5)}^{m + 2} \times {( - 5)}^{6} = {( - 5)}^{10}$

$\rm :\longmapsto\: {( - 5)}^{m + 2 + 6} = {( - 5)}^{10}$

$\rm :\longmapsto\: {( - 5)}^{m + 8} = {( - 5)}^{10}$

$\rm :\implies\:m + 8 = 10$

$\rm :\implies\:m \: = \: 2$