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 …

Question

asked Feb 27, 2018 51.9k views

2 Answers

Jckly · Answer 1 · 2018-03-04T16:03:27+0000

C - the fourth root of 2

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 =
$\frac{2^{(3)/(4) }}{2^{(1)/(2) }}$

Now, we are going to use the law of exponents for division:
(a^m)/(a^n) =a^(m-n)

We can infer from our expression that
a=2 ,
m=(3)/(4) , and
n=(1)/(2) , so let's use our rule:

$\frac{2^{(3)/(4) }}{2^{(1)/(2) }}=2^{(3)/(4)-(1)/(2) }}=2^{(1)/(4)}$

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

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

$2^{(1)/(4)}=\sqrt[4]{2}$

Or in words: the fourth root of 2.