### About Fractional 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

#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:

Solutions:

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

b) $$729$$

c) $$4$$

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#2:

Solutions:

a) $$729$$

b) $$64$$

c) $$100{,}000$$

d) $$9$$

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#3:

Solutions:

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

b) $$x^{12}$$

c) $$7b$$

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#4:

Solutions:

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

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

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#5:

Solutions:

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