If 16-8n-2-2m- find the value of m

Finding the value of m:[ 16×8^n+2=2^m; ⇒(2)^4×(2^3)^n+2=2^m; ⇒(2)^4×(2^3n+6)=2^m(∵(a^m)^n=a^mn); ⇒(2)^4+(3n+6)=2^m(∵a^m×a^n ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

If 16×8n+2=2m...

Question

If $16 \times 8^{n + 2} = 2^{m}$ , find the value of $m$

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Solution

Finding the value of $m$ :
$\begin{array}{l} 16 \times 8^{n + 2} = 2^{m} \\ \Rightarrow {(2)}^{4} \times {(2^{3})}^{n + 2} = 2^{m} \\ \Rightarrow {(2)}^{4} \times (2^{3 n + 6}) = 2^{m} (∵ {(a^{m})}^{n} = a^{m n}) \\ \Rightarrow {(2)}^{4 + (3 n + 6)} = 2^{m} (∵ a^{m} \times a^{n} = a^{m + n}) \\ \Rightarrow {(2)}^{10 + 3 n} = 2^{m} \\ \Rightarrow 10 + 3 n = m \end{array}$
Hence,the value of $m = 3 n + 10$

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$(i i i) {(m^{2} - n^{2})}^{2}$ [3 MARKS]

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If 16×8n+2=2m, find the value of m

Finding the value of m:16×8n+2=2m⇒24×23n+2=2m⇒24×23n+6=2m∵amn=amn⇒24+3n+6=2m∵am×an=am+n⇒210+3n=2m⇒10+3n=mHence,the value of m=3n+10

If $16 \times 8^{n + 2} = 2^{m}$ , find the value of $m$