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

This math topic focuses on the simplification of negative fractional exponents with square integer bases. Students practice factoring bases and applying negative fractional exponents to them. It includes problems revolving around integer bases like 36, 25, 16, 9, and 4, which are processed with exponents like -1/2. Students aim to factorize these bases and express them in exponent form to simplify the expressions effectively. A range of possible factorizations and simplifications provides multiple-choice answers, where students need to select the correct simplified form.

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

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Negative Fractional Exponents with 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

25(−12)25^{(\frac{-1}{2})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Factored Exponent (Level 1)'. Part of a broader unit on 'Exponents - Negative Bases and Exponents - Practice' Learn online: app.mobius.academy/math/units/exponents_negative_bases_and_exponents_practice/
1
Factor the base number and simplify to make it easier to solve
A LaTex expression showing 4 to the power of (-1 over 2 )
a A LaTex expression showing 1 over (2 times 2) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (2 times 2 times 13) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (2 times 2 times 11) to the power of (\frac{1 {2 )}}
d A LaTex expression showing 1 over (2 times 2 times 2) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 7) 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 36 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) 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 3 times 3) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 9) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 3 times 3 times 11) 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 11) to the power of (\frac{1 {2 )}}
b A LaTex expression showing 1 over (3 times 3 times 13) to the power of (\frac{1 {2 )}}
c A LaTex expression showing 1 over (3 times 3 times 3) 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) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (3 times 3 times 7) to the power of (\frac{1 {2 )}}
4
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 2) 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 2 times 2) to the power of (\frac{1 {2 )}}
e A LaTex expression showing 1 over (2 times 2 times 2 times 2 times 3) to the power of (\frac{1 {2 )}}
f A LaTex expression showing 1 over (2 times 2 times 4) to the power of (\frac{1 {2 )}}
5
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 7) 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 (5 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 11) to the power of (\frac{1 {2 )}}