Find the value of p such that- -13-2p-8- - dfrac -1-13-14-13103

-13-2p-8-1-13-x2212-2p-8-1-13-x2212-14-x2234-x2212-2p-8-x2212-14-x2234-2p-8-14-x2234-2p-6-x2234-p-3So- option D is correct-

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Standard X

Mathematics

Question

Find the value of $p$ such that, $(13)^{2 p + 8} = \frac{1}{(13)^{- 14}}$
$13$
$1$
$0$
$3$

1

13

0

3

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Solution

Verified by Toppr

$(13)^{2 p + 8} = \frac{1}{(13)^{- (2 p + 8)}} = \frac{1}{(13)^{- 14}}$
$∴ - (2 p + 8) = - 14$
$∴ (2 p + 8) = 14$
$∴ 2 p = 6$
$∴ p = 3$

So, option $D$ is correct.

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Find the value of $p$ such that, $(13)^{2 p + 8} = \frac{1}{(13)^{- 14}}$
$13$
$1$
$0$
$3$

$(13)^{2 p + 8} = \frac{1}{(13)^{- (2 p + 8)}} = \frac{1}{(13)^{- 14}}$
$∴ - (2 p + 8) = - 14$
$∴ (2 p + 8) = 14$
$∴ 2 p = 6$
$∴ p = 3$

So, option $D$ is correct.