evaluate. write your answer as a whole number or as a simplified fraction. \\(\\frac{9^{-1}}{4^{-4}} =…
evaluate. write your answer as a whole number or as a simplified fraction. \\(\\frac{9^{-1}}{4^{-4}} = \\frac{\\quad}{\\quad}\\)
Answer
Explanation:
Step1: Rewrite negative exponents
Recall $a^{-n}=\frac{1}{a^n}$, so: $9^{-1}=\frac{1}{9}$, $4^{-4}=\frac{1}{4^4}$ The expression becomes $\frac{\frac{1}{9}}{\frac{1}{4^4}}$
Step2: Simplify complex fraction
Dividing by a fraction is multiplying by its reciprocal: $\frac{\frac{1}{9}}{\frac{1}{4^4}} = \frac{1}{9} \times 4^4$
Step3: Calculate $4^4$
$4^4=4\times4\times4\times4=256$ The expression is $\frac{256}{9}$
Answer:
$\frac{256}{9}$