The correct option is D 8^ 15(8^2/8^5)^4 nbsp;× 8^ 3= (8^2 5)^4 nbsp;× 8^ 3 (∵a^m/a^n=a^m n) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbs ...

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Exponent of an Exponent

82/834× 8-3=-

Question

$(\frac{8^{2}}{8^{5}})^{4} \times 8^{- 3}$ = ___

8^{2}

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8^{25}

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8^{- 10}

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8^{- 15}

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Solution

The correct option is D $8^{- 15}$
$(\frac{8^{2}}{8^{5}})^{4} \times 8^{- 3} = (8^{2 - 5})^{4} \times 8^{- 3} (∵ \frac{a^{m}}{a^{n}} = a^{m - n})$
$= (8^{- 3})^{4} \times 8^{- 3}$
$= 8^{- 12} \times 8^{- 3} (∵ (a^{m})^{n} = a^{m n})$
$= 8^{- 15} (∵ a^{m} \times a^{n} = a^{m + n})$

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