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c)
16^(-x)=(1)/(64)

c) $16^{-x}=\frac{1}{64}$

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Evaluate rational exponents

Full solution

Q. c)

16^{-x}=\frac{1}{64}

Rewrite as Power of $16$ : Rewrite $\frac{1}{64}$ as a power of $16$ to compare exponents. $\newline$ $\frac{1}{64} = 16^{-1}$ because $16 = 2^4$ and $64 = 2^6$ , so $64 = 16^{\frac{6}{4}}$ which simplifies to $16^{\frac{3}{2}}$ , and the reciprocal is $16^{-\frac{3}{2}}$ .
Set Exponents Equal: Set the exponents equal to each other since the bases are the same. $\newline$ - $x = -\frac{3}{2}$
Solve for x: Solve for x by multiplying both sides by $-1$ . $\newline$ $x = \frac{3}{2}$

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