Question

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

Answer 1

Answer

C - the fourth root of 2

Explanation

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.

Answer 2

Answer:

C

Step-by-step explanation: