Question

algebra i b - mrs. mary congleton 25 - 26 exponential functions with radical bases which is equivalent to ( 64^{\frac{1}{2}} )? ( 16sqrt4{4} ) ( 2sqrt4{4} ) ( 16 ) ( 4 )

Explanation:

Step1: Rewrite 64 as power of 4

$64 = 4^3$

Step2: Apply exponent power rule

$(4^3)^{\frac{1}{3}} = 4^{3 \times \frac{1}{3}}$

Step3: Simplify the exponent

$4^{3 \times \frac{1}{3}} = 4^1 = 4$

Step4: Verify other options (optional check)

$16\sqrt[3]{4}=16 \times 4^{\frac{1}{3}}
eq 4$; $2\sqrt[3]{4}=2 \times 4^{\frac{1}{3}}
eq 4$; $16
eq 4$

Answer:

4