If \(x = 5^{25}\) and \(x^x = 5^k,\) what is \(k?\)

[M7MBA]

If \(x = 5^{25}\) and \(x^x = 5^k,\) what is \(k?\)

A. \(5^{26}\)
B. \(5^{27}\)
C. \(5^{50}\)
D. \(5^{52}\)
E. \(5^{625}\)

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

[Jay@ManhattanReview]

If \(x = 5^{25}\) and \(x^x = 5^k,\) what is \(k?\)

A. \(5^{26}\)
B. \(5^{27}\)
C. \(5^{50}\)
D. \(5^{52}\)
E. \(5^{625}\)

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

So, we have \(x = 5^{25}\) and \(x^x = 5^k,\)

Let's raise the power of \(x\) to \(x = 5^{25}\), we get \(x^x = 5^{25^x} = 5^{25x} = 5^k\)

\(=> 25x = k\)

Replacing the value of \(x\), we get \(25*5^{25} = k\)

\(k=5^2*5^{25} = 5^{27}\)

Correct answer: B

Hope this helps!

-Jay
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