Find the Value of (8p)P If 9p + 2 - 9p = 240. - Mathematics

Find the value of (8p)^p if 9^{p + 2} - 9^p = 240.

बेरीज

9^p+2- 9^p = 240
⇒ 9^p (9² - 1) = 240
⇒ 9^{p (}80) = 240
⇒ 9^p = 3
⇒ 3^2p= 3
⇒ 2p = 1
⇒ p = `(1)/(2)`
(8p)^p = (2³p)^p

= `(2^3 . 1/2)^(1/2)`

= `(2^(3-1 .))^(1/2)`

= `(2^2)^(1/2)`
= 2.

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