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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

Verified Answer :

JcAlmighty

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.

ajuniorb2018

Answer:

4th rout of 2

Step-by-step explanation:

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