Question

simplify. 16^{-\frac{3}{4}}

Explanation:

Step1: Rewrite 16 as a power of 2

$16 = 2^4$, so $16^{-\frac{3}{4}}=(2^4)^{-\frac{3}{4}}$

Step2: Apply power - of - a - power rule

According to $(a^m)^n=a^{mn}$, we have $(2^4)^{-\frac{3}{4}}=2^{4\times(-\frac{3}{4})}$

Step3: Calculate the exponent

$4\times(-\frac{3}{4})=- 3$, so $2^{4\times(-\frac{3}{4})}=2^{-3}$

Step4: Use the negative - exponent rule

$a^{-n}=\frac{1}{a^n}$, then $2^{-3}=\frac{1}{2^3}$

Step5: Calculate the denominator

$2^3 = 8$, so $\frac{1}{2^3}=\frac{1}{8}$

Answer:

$\frac{1}{8}$