Question

Which factors of the base would help simplify the expression 16^1/4

16 = 4*2*2
16 = 2*2*2*2
16 = 8*8
16 = 4*4

Answer 1

Just choose one of the answers

Answer 2

To simplify the expression \( 16^{1/4} \), it's helpful to express 16 as a power of its prime factors. The most straightforward representation is:

\[
16 = 2^4
\]

Now, substituting this into the expression:

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

Using the power of a power property of exponents, you multiply the exponents:

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

So, \( 16^{1/4} = 2 \).

To address your initial question about which factors of the base would help simplify the expression, the most relevant representation is expressing 16 as \( 2^4 \). This allows for straightforward exponent manipulation and simplification. None of the other representations you provided (like \( 4 \times 4 \) or \( 8 \times 8 \)) simplify the expression as effectively.

Thus, the key factor that helps in this case is:

\[
16 = 2^4
\]

Answer 3

The best choice is:

**16 = 2 * 2 * 2 * 2.**

This clearly shows that \( 16 = 2^4 \), which simplifies \( 16^{1/4} \) effectively.