Rewrite the rational exponent as a radical by extending the properties of integers exponents. 8 radical2^3 , Radical 2^3/4 ,4 radical 2 or radical2

Question

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

2^3/4 / 2^1/2

 

 

The choices are

 

8 radical2^3

 

Radical 2^3/4

 

4 radical 2

 

radical2

Answer 1

Use laws of exponents. a^m/ aⁿ = a^m-n . If you have like bases and you are dividing the expression then to simplify you subtract their exponents. If you were multiplying like bases then you add the exponents.
So 2 is your like base and since were dividing we subtract their exponents. 2^3/4-1/2 = 2^1/4. ( I'm assuming you know how to subtract fractions with different denominators). Now you just have to rewrite it as a radical. Your Index is the denominator in the rational exponent and the power of the base 2 is the numerator which happens to be 1. so your answer should be The fourth root of 2.