﻿ GreeneMath.com - Using Fractional Exponents Test
Fractional Exponents Test

In some cases, fractional exponents allow us to work with radicals more easily. Most commonly, this allows us to write the square root of a number or expression as being raised to the power of one - half. Similarly, when we take the cube root of a number or expression, this is the same as being raised to the power of one - third.

Test Objectives:

•Demonstrate the ability to simplify an expression raised to the power of 1/n

•Demonstrate the ability to simplify an expression raised to the power of m/n

•Demonstrate the ability to report a simplified answer that contains no fractional exponents in the denominator

Using Fractions as Exponents Test:

#1:

Instructions: Simplify, report your answer with no fractional exponents in the denominator.

a) $$32^{-\frac{3}{5}}$$

b) $$243^\frac{6}{5}$$

c) $$16^\frac{1}{2}$$

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#2:

Instructions: Simplify, report your answer with no fractional exponents in the denominator.

a) $$81^\frac{3}{2}$$

b) $$16^\frac{3}{2}$$

c) $$10,000^\frac{5}{4}$$

d) $$27^\frac{2}{3}$$

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#3:

Instructions: Simplify, report your answer with no fractional exponents in the denominator.

a) $$(n^6)^{-\frac{3}{2}}$$

b) $$(x^{16})^\frac{3}{4}$$

c) $$(343b^3)^\frac{1}{3}$$

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#4:

Instructions: Simplify, report your answer with no fractional exponents in the denominator.

a) $$(ab^2)^{-\frac{1}{2}} \cdot (ba^\frac{1}{3})^\frac{3}{2}$$

b) $$(xy^\frac{1}{3})(y^2)^{-2}$$

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#5:

Instructions: Simplify, report your answer with no fractional exponents in the denominator.

a) $$\frac{(x^\frac{3}{2}z^{-1}y^{-1}z^\frac{3}{2})^\frac{5}{4}}{yx^\frac{3}{2}}$$

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Written Solutions:

#1:

Solution:

a) $$\frac{1}{8}$$

b) $$729$$

c) $$4$$

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#2:

Solution:

a) $$729$$

b) $$64$$

c) $$100,000$$

c) $$9$$

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#3:

Solution:

a) $$\frac{1}{n^9}$$

b) $$x^{12}$$

c) $$7b$$

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#4:

Solution:

a) $$b^\frac{1}{2}$$

b) $$\frac{xy^\frac{1}{3}}{y^4}$$

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#5:

Solution:

a) $$\frac{x^\frac{3}{8}z^\frac{5}{8}y^\frac{3}{4}}{y^3}$$

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