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) $$16^\frac{1}{2}$$
#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) $$27^\frac{2}{3}$$
#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) $$(343b^3)^\frac{1}{3}$$
#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) $$(xy^\frac{1}{3})(y^2)^{-2}$$
#5:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$\frac{(x^\frac{3}{2}z^{-1}y^{-1}z^\frac{3}{2})^\frac{5}{4}}{yx^\frac{3}{2}}$$
Written Solutions:
Solution:
a) $$\frac{1}{8}$$
b) $$729$$
c) $$4$$
Solution:
a) $$729$$
b) $$64$$
c) $$100,000$$
d) $$9$$
Solution:
a) $$\frac{1}{n^9}$$
b) $$x^{12}$$
c) $$7b$$
Solution:
a) $$b^\frac{1}{2}$$
b) $$\frac{xy^\frac{1}{3}}{y^4}$$
Solution:
a) $$\frac{x^\frac{3}{8}z^\frac{5}{8}y^\frac{3}{4}}{y^3}$$