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eduard
3 years ago
5

Rewrite the rational exponent as a radical by extending the properties of integer exponents. (2 points) 2 to the 3 over 4 power,

all over 2 to the 1 over 2 power
A - the eighth root of 2 to the third power
B - the square root of 2 to the 3 over 4 power
C - the fourth root of 2
D - the square root of 2
Mathematics
2 answers:
icang [17]3 years ago
4 0

Answer:

The answer is C) The fourth root of 2

I took the quiz and that is the definite answer. The correct answer. ;)


yKpoI14uk [10]3 years ago
4 0
<h2>Answer</h2>

C - the fourth root of 2

<h2>Explanation</h2>

First, we are going to write our expression in mathematical notation:

2 to the 3 over 4 power, all over 2 to the 1 over 2 power = \frac{2^{\frac{3}{4} }}{2^{\frac{1}{2} }}

Now, we are going to use the law of exponents for division: \frac{a^m}{a^n} =a^{m-n}

We can infer from our expression that a=2, m=\frac{3}{4}, and n=\frac{1}{2}, so let's use our rule:

\frac{2^{\frac{3}{4} }}{2^{\frac{1}{2} }}=2^{\frac{3}{4}-\frac{1}{2} }}=2^{\frac{1}{4}}

Finally, we are going to use the rule for fractional exponents: a^{\frac{1}{n} }=\sqrt[n]{a}

Just like before, we can infer that a=2 and n=4, so let's use our rule:

2^{\frac{1}{4}}=\sqrt[4]{2}

Or in words: the fourth root of 2.

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