Rational Exponents Quick Check

1 of 51 of 5 Items
Question
Which factors of the base would help simplify the expression 1614
?(1 point)
Responses

16=4⋅2⋅2
16 equals 4 times 2 times 2

16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2

16=4⋅4
16 equals 4 times 4

16=8⋅8
16 equals 8 times 8
Skip to navigation

1 answer

To simplify the expression \( 16^{\frac{1}{4}} \), it is helpful to express 16 in a way that makes it easier to work with its base factors.

The best factorization among the options provided is:

16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 (which can also be written as \( 16 = 2^4 \))

Using this factorization, we can rewrite \( 16^{\frac{1}{4}} \):

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

Thus, the correct response for simplifying the expression would be:

16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 (16 equals 2 times 2 times 2 times 2).