Rational Exponents Quick Check

Question

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

16=4⋅4
16 equals 4 times 4

16=8⋅8
16 equals 8 times 8

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

16=4⋅2⋅2

Answer 1

To simplify the expression \(16^{\frac{1}{4}}\), we want to express \(16\) in a way that makes it easier to work with.

Given the options, the factorization of \(16\) that would be most useful is:

• \(16 = 2 \cdot 2 \cdot 2 \cdot 2\), which can also be written as \(16 = 2^4\).

This factorization reflects the fact that \(16\) is \(2\) raised to the power of \(4\), which directly relates to the rational exponent \( \frac{1}{4} \).

So, from the options provided, the best choice is:

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