Question
Rational Exponents Quick Check
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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
Answers
GPT-4o mini
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).
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).