Simplify $(16^{12x})^{\frac{5}{48x}}$ . Answer _ Express $5^{-2}$ as a percentage. Answer _

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Worked solution

1. Apply the power of a power law to combine the exponents.

$(16^{12x})^{\frac{5}{48x}}=16^{12x\times \frac{5}{48x}}$

2. Simplify the exponent and evaluate the resulting power.

$12x\times \frac{5}{48x}=\frac{60x}{48x}=\frac54$

So
$(16^{12x})^{\frac{5}{48x}}=16^{\frac54}=(2^4)^{\frac54}=2^5=32.$

Answer

$32$

1. Evaluate the negative power and convert it to a percentage.

$5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{25}=0.04=4\%$

Answer

$4\%$

AI analysis — may contain mistakes.

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