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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent (Level 1)

This math topic practices various skills involving negative fractional exponents. Specifically, it focuses on evaluating expressions where non-square integer bases are raised to negative fractional powers. Students are asked to factor the base numbers and simplify the expressions to make them easier to solve. Each problem involves identifying the correct simplified form of an exponent expression, which helps in enhancing their understanding of exponentiation, factoring, and simplification of algebraic expressions involving radicals.

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

36(−12)36^{(\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 1)'. 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 72 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) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 9) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 3 times 3 times 11) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (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 2 times 3 times 3 times 7) to the power of (\frac{1 {2 )}}
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 times 3) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 3 times 3 times 3) 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 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 3 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 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 80 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5 times 13) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 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 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 4 times 2 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 4 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 54 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 3 times 3 times 3 times 13) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) 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 )}}
5
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 4 times 2) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2) 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 13) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 7) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 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 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 6 times 3) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 3) 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 2 times 3 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 9) to the power of (\frac{1 {2 )}}
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) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 3 times 3 times 7) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 3 times 3 times 13) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 3 times 3 times 11) 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 )}}