Question

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

Explanation:

Step1: Rewrite 16 as a power

$16 = 2^4$, 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: Evaluate $2^3$

$2^3=2\times2\times2 = 8$

Answer:

8