If 4 m -2- 2-4-24- then m -A- 2B- 4C- 8D- 1-2

The correct option is A 2Note that (a^m)^n=a^mn 4^m+2=(2^2)^m+2=2^2(m+2)=2^2m+4 Now since a^m × a^n = a^m+n So, 2^2m+4 × 2^ 4 = 2^2m+4 4 = 2^2m 2^2m = 2^4 Equat ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

If 4 m +2× 2-...

Question

If $4^{m + 2}$ $\times$ $2^{- 4}$ = $2^{4}$ , then $m$ =

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\frac{1}{2}

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Solution

The correct option is A 2
Note that $(a^{m})^{n} = a^{m n}$
$⟹ 4^{m + 2} = (2^{2})^{m + 2} = 2^{2 (m + 2)} = 2^{2 m + 4}$
Now since $a^{m}$ $\times$ $a^{n}$ = $a^{m + n}$
So, $2^{2 m + 4}$ $\times$ $2^{- 4}$ = $2^{2 m + 4 - 4}$ = $2^{2 m}$
$⟹ 2^{2 m}$ = $2^{4}$
Equating the exponents, $2 m = 4 \Rightarrow m = 2$

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If 4m+2 × 2−4 = 24 , then m =

The correct option is A 2Note that (am)n=amn ⟹4m+2=(22)m+2=22(m+2)=22m+4 Now since am × an = am+n So, 22m+4 × 2−4 = 22m+4−4 = 22m ⟹22m = 24 Equating the exponents, 2m=4⇒m=2

If $4^{m + 2}$ $\times$ $2^{- 4}$ = $2^{4}$ , then $m$ =