Question

If (9^2)p = 9^8, what is the value of p?
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6

Answer 1

is p also a power of that 9^2 term?

Answer 2

Yes @DanJS

Answer 3

\[[9^2]^p = 9^8\]

Answer 4

recall, a power raised to a power is simplified by multiplying the powers

[9^2]^p = 9^(2*p)

Answer 5

Since you have the same bases raised to different powers, you can equate the powers from both sides

2p = 8

Answer 6

Or if you need work, take the log base 9 of both sides, move the powers down in front...

Answer 7

So its D? Or did I do my math wrong?

Answer 8

2p = 8

Answer 9

\[9^{2p}=9^8\]

\[\log_{9}9^{2p} = \log_{9}9^8 \]

\[(2p)*\log_{9}9 = 8 * \log_{9}9\]

\[2p * 1 = 8*1~~~~~~~~~~~;p=4\]