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If 16a=64^b , then what is a in terms of b?

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If 16a=64^b , then what is a in terms of b? [#permalink] New post   31 Jan 2024, 03:59
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If \(16a=64^b\) , then what is a in terms of b?

A. \(4^b\)

B. \(2^{\frac{6b}{4}\)

C. \(2^{6b-4}\)

D. \(4^{\frac{6b}{4}}\)

E. \(4^{6b-4}\)


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If 16a=64^b , then what is a in terms of b? [#permalink] New post   31 Jan 2024, 10:45
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Make the bases on both sides of the equation the same.

\(16a = (2^4)a\)

\(64^b = (2^6)^b = 2^{6b}\)

\(2^{4}a = 2^{6b}\)

Use exponent operations involving same bases to simplify.

\(a = \frac{2^{6b}}{2^4} = 2^{6b-4}\)
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If 16a=64^b , then what is a in terms of b? [#permalink]
31 Jan 2024, 10:45
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