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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Factor the base number and simplify to make it easier to solve

45(−12)45^{(\frac{-1}{2})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent (Level 2)'. Part of a broader unit on 'Exponents - Negative and Fractional Bases and Exponents' Learn online: app.mobius.academy/math/units/exponents_negative_and_fractional_bases_review/
1
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 250 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 25 times 5) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 5 times 5 times 5) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (5 times 5 times 5) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 5 times 5 times 5 times 5) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 5 times 25) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 5 times 5 times 5 times 7) to the power of (\frac{1 {3 )}}
2
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 108 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 3 times 3) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 9 times 3) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (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 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 40 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 5) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 2 times 5) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 5 times 5) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 2 times 10) to the power of (\frac{1 {3 )}}
4
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 24 to the power of (-1 over 3 )
a A LaTex expression showing 1 over (2 times 2 times 3) to the power of (\frac{1 {3 )}}
b A LaTex expression showing 1 over (2 times 4 times 3) to the power of (\frac{1 {3 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 3) to the power of (\frac{1 {3 )}}
d A LaTex expression showing 1 over (2 times 2 times 6) to the power of (\frac{1 {3 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 5) to the power of (\frac{1 {3 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3) to the power of (\frac{1 {3 )}}
5
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 45 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (3 times 3 times 5) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (3 times 3 times 5 times 11) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (3 times 3 times 5 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (3 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (3 times 3 times 5 times 7) to the power of (\frac{1 {2 )}}
6
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 48 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3 times 7) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 6) 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 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 4 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
7
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 2 times 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 2 times 2 times 2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 4 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 3 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 4 times 3 times 3) to the power of (\frac{1 {2 )}}