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

2^3/4 / 2^1/2

2^3/4 / 2^1/2

The choices are

8 radical2^3

Radical 2^3/4

4 radical 2

radical2

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

2^3/4 / 2^1/2

2^3/4 / 2^1/2

The choices are

8 radical2^3

Radical 2^3/4

4 radical 2

radical2

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Los Angeles, CA

Use laws of exponents. a^{m}/ a^{n} = 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.

So 2 is your like base and since were dividing we subtract their exponents. 2

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