Question

Find the value of m 9m÷3 to the power -2 =9 to the power 4​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given an algebric Equation
• $\sf{{\dfrac{9m}{3}}^{-2} = 9^4}$

To Find:

• We have to find the value of m

Solution:

$\underline{\large\mathfrak\red{We \: have \: been \: given \: that}}$

$\hookrightarrow \sf{{\dfrac{9m}{3}}^{-2}=9^4 }$

$\hookrightarrow \sf{{3m}^{-2}=9^4 }$

Using law of exponents

$\boxed{\sf{\orange{{\dfrac{1}{a}}^m = a^{-m}}}}$

$\hookrightarrow \sf{{\left ( \dfrac{1}{3m} \right ) }^{2}=9^4 }$

$\hookrightarrow \sf{\dfrac{1}{9m^2}=9^4 }$

Cross Multiplying the terms

$\hookrightarrow \sf{\dfrac{1}{m^2}=9^4 \times 9}$

$\hookrightarrow \sf{\dfrac{1}{m^2}=9^5 }$

Reciprocaling Both sides

$\hookrightarrow \sf{m^2 = {\left ( \dfrac{1}{9} \right ) }^5}$

$\hookrightarrow \sf{m^2 = {\left ( \dfrac{1}{3^2} \right ) }^5}$

$\hookrightarrow \sf{m^2 = {\left ( \dfrac{1}{3^5} \right ) }^2}$

Comparing Bases on Both sides

$\hookrightarrow \sf{m = \dfrac{1}{3^5}}$

$\hookrightarrow \boxed{\sf{m = \dfrac{1}{243}}}$

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$\huge\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}$

$\large \boxed{\sf{\purple {Value \: of \: m = \dfrac{1}{243}}}}$

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$\huge\mathfrak\green{Verification:}$

Taking LHS

$\implies \sf{{\dfrac{9m}{3}}^{-2}}$

$\implies \sf{(3m)^{-2}}$

Putting m = 1/243

$\implies \sf{(3m)^{-2}}$

$\implies \sf{{\left ( 3 \times \dfrac{1}{243} \right ) }^{-2}}$

$\implies \sf{{\dfrac{1}{81}}^{-2}}$

Using : $\implies \boxed{\sf{\orange{{\dfrac{1}{a}}^m = a^{-m}}}}$

$\implies \sf{81^2}$

$\implies \sf{(9^2)^2}$

$\implies \sf{9^4 = RHS}$

Hence Verified !