Which factors of the base would help simplify the expression 16^1/4 ?(1 point)

Question

Responses

A) 16=4⋅2⋅2
16 equals 4 times 2 times 2

B) 16=8⋅8
16 equals 8 times 8

C) 16=4⋅4
16 equals 4 times 4

D) 16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2

Answer 1

To simplify the expression \( 16^{1/4} \), we can consider the factorization of 16.

The correct option is:

D) \( 16 = 2 \cdot 2 \cdot 2 \cdot 2 \)

This option shows that 16 can be expressed as \( 2^4 \). When we apply the exponent \( \frac{1}{4} \):

\[ 16^{1/4} = (2^4)^{1/4} = 2^{(4 \cdot \frac{1}{4})} = 2^1 = 2 \]

This simplification is most straightforward when expressing 16 as \( 2^4 \).