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Fractional Exponents Test
About Using Fractions as Exponents:

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) $$100,000$$


d) $$9$$


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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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