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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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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 100 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 5 times 5) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 25) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 5 times 5 times 11) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 5 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 10 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 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 80 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5 times 13) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 4 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 4 times 2 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 5) to the power of (\frac{1 {2 )}}
3
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 96 to the power of (-1 over 2 )
a 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 {2 )}}
b A LaTex expression showing 1 over (2 times 4 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 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 2 times 3 times 13) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 3 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
4
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 3 times 3 times 11) 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) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 2 times 9) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (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 times 7) 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 )}}
5
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 12 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 3) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (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 3 times 7) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 3 times 5) 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 3 times 13) to the power of (\frac{1 {2 )}}
6
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 20 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2 times 3 times 5) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 5 times 7) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 5 times 11) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 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 )}}
7
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 5 times 5 times 13) 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 2 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 (2 times 5 times 5 times 7) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 5 times 5 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 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 (3 times 3 times 5 times 5) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (3 times 3 times 5 times 7) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (3 times 3 times 3 times 5) to the power of (\frac{1 {2 )}}