Allday Education

Free Rational Exponents Worksheet

Ten rational-exponent problems (fractional powers) with an exact answer key.

Answer key included
Name: Date:
Rational Exponents
1.
25634\displaystyle 256^{\frac{3}{4}}
2.
452\displaystyle 4^{\frac{5}{2}}
3.
8114\displaystyle 81^{\frac{1}{4}}
4.
1614\displaystyle 16^{\frac{1}{4}}
5.
932\displaystyle 9^{\frac{3}{2}}
6.
2713\displaystyle 27^{\frac{1}{3}}
7.
2552\displaystyle 25^{\frac{5}{2}}
8.
21653\displaystyle 216^{\frac{5}{3}}
9.
129614\displaystyle 1296^{\frac{1}{4}}
10.
952\displaystyle 9^{\frac{5}{2}}
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Rational Exponents
1.
25634\displaystyle 256^{\frac{3}{4}}
Answer: 6464
2.
452\displaystyle 4^{\frac{5}{2}}
Answer: 3232
3.
8114\displaystyle 81^{\frac{1}{4}}
Answer: 33
4.
1614\displaystyle 16^{\frac{1}{4}}
Answer: 22
5.
932\displaystyle 9^{\frac{3}{2}}
Answer: 2727
6.
2713\displaystyle 27^{\frac{1}{3}}
Answer: 33
7.
2552\displaystyle 25^{\frac{5}{2}}
Answer: 31253125
8.
21653\displaystyle 216^{\frac{5}{3}}
Answer: 77767776
9.
129614\displaystyle 1296^{\frac{1}{4}}
Answer: 66
10.
952\displaystyle 9^{\frac{5}{2}}
Answer: 243243
Andy · alldayeverydaymath.com

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About this worksheet

Students evaluate expressions like 8 to the two-thirds by reading the denominator as a root and the numerator as a power. The bridge between radicals and exponent rules in Algebra 2.

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