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Exponents

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

This math topic focuses on practicing how to handle negative fractional exponents with non-square integer bases. It involves exercises where students factorize the base numbers and simplify expressions that incorporate negative fractional powers. Each question prompts learners to choose from multiple possible simplified forms of a given expression, testing their understanding of exponent rules and factorization. The complexity highlights manipulating fractional negative exponents with different integer base configurations.

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

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

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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent
1
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 50 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 3 times 5 times 5) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 5 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 5 times 5 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 5 times 5 times 7) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 5 times 5 times 13) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 5 times 5) to the power of (\frac{1 {2 )}}
2
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 36 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 7) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 9) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 11) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 6 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {2 )}}
3
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 75 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (3 times 5 times 5 times 13) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (3 times 5 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (3 times 3 times 5 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 3 times 5 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (3 times 5 times 5 times 7) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (3 times 5 times 5 times 5) to the power of (\frac{1 {2 )}}
4
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 144 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 4 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 4 times 3 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}
e 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 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
5
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 54 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 3 times 3 times 3 times 13) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 3 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 3 times 3) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 9 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 3 times 3 times 3) to the power of (\frac{1 {2 )}}
6
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 54 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 3 times 3 times 3 times 13) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (2 times 3 times 9) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 3 times 3 times 3 times 5) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 9 times 3) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 3 times 3 times 3) to the power of (\frac{1 {3 )}}
7
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 18 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 3 times 3 times 7) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 3 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 3 times 3 times 11) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 3 times 3 times 3) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 3 times 3 times 13) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
8
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 times 13) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 4 times 2) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 7) to the power of (\frac{1 {2 )}}