Question

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 3 over 4 power, all over 2 to the 1 over 2 power

the eighth root of 2 to the third power - THIS ONE
the square root of 2 to the 3 over 4 power
the fourth root of 2
the square root of 2

Answer 1

The answer is the fourth root of 2.

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

So, use the rule: $\frac{x^{a} }{ x^{b} } = x^{a-b}$
$\frac{2^{ \frac{3}{4} } }{2^{ \frac{1}{2} }} = 2^{\frac{3}{4}- \frac{1}{2}}= 2^{\frac{3}{4}- \frac{1*2}{2*2}}= 2^{\frac{3}{4}- \frac{2}{4}}= 2^{ \frac{3-2}{4} } = 2^{ \frac{1}{4} }$

Now, use the rule: $a^{ \frac{m}{n}} = \sqrt[n]{ x^{m} }$
$2^{ \frac{1}{4} } = \sqrt[4]{ 2^{1} }= \sqrt[4]{2}$
which is the same as the fourth root of 2.

Answer 2

Answer:

4th rout of 2

Step-by-step explanation:

I did this quiz before