Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent (Level 2)

This math topic focuses on practicing the simplification of negative fractional exponents with squared integer bases. Students will gain skills in factoring base numbers and simplifying expressions to solve problems related to negative bases and exponents. Each problem presents an integer base with a negative fractional exponent for students to factor and simplify, often provided with multiple-choice answers for better comprehending factorization and exponentiation principles within the broader unit of negative bases and exponents.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent Worksheet

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Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent
1
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 216 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3 times 3 times 11) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3 times 3 times 13) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 9 times 3) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {3 )}}
2
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 16 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 4) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {2 )}}
3
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 9 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (3 times 3 times 7) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (3 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (3 times 3 times 13) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (3 times 3 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (3 times 3 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (3 times 3 times 11) to the power of (\frac{1 {2 )}}
4
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 64 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 4) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (2 times 2 times 4 times 2 times 2) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 2 times 13) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {3 )}}
5
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 81 to the power of (-1 over 4 )
a A LaTex expression showing 1 over (3 times 3 times 3 times 3 times 5) to the power of (\frac{1 {4 )}}
b A LaTex expression showing 1 over (3 times 3 times 9) to the power of (\frac{1 {4 )}}
c A LaTex expression showing 1 over (3 times 3 times 3) to the power of (\frac{1 {4 )}}
d A LaTex expression showing 1 over (3 times 9 times 3) to the power of (\frac{1 {4 )}}
e A LaTex expression showing 1 over (3 times 3 times 3 times 3 times 11) to the power of (\frac{1 {4 )}}
f A LaTex expression showing 1 over (3 times 3 times 3 times 3) to the power of (\frac{1 {4 )}}
6
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 125 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (5 times 5 times 5 times 7) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (5 times 5 times 5 times 11) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (3 times 5 times 5 times 5) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (5 times 5 times 5) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 5 times 5 times 5) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (5 times 5 times 5 times 5) to the power of (\frac{1 {3 )}}
7
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 16 to the power of (-1 over 4 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 2) to the power of (\frac{1 {4 )}}
b A LaTex expression showing 1 over (2 times 4 times 2) to the power of (\frac{1 {4 )}}
c A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {4 )}}
d A LaTex expression showing 1 over (2 times 2 times 4) to the power of (\frac{1 {4 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {4 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {4 )}}
8
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 25 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (5 times 5 times 11) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (5 times 5 times 7) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (3 times 5 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (5 times 5 times 13) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (5 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (5 times 5 times 5) to the power of (\frac{1 {2 )}}