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

This math topic focuses on practicing how to work with negative fractional exponents involving non-square integer bases, specifically by factoring the base number and expressing the result as a radical. Each problem presents an integer raised to the power of a negative fractional exponent, and students are required to simplify these expressions by breaking down the base number into its prime factors and converting the exponentiation into a radical form. Multiple choice answers are provided for students to ascertain the correct simplified expression. This is part of a broader unit on negative bases and exponents.

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 Radical

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

Factor this exponent's base number and express it as a radical

36(−12)36^{(\frac{-1}{2})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical (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 this exponent's base number and express it as a radical
A LaTex expression showing 45 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 3 times 3 times 5
b A LaTex expression showing 1 over square root of 3 times 3 times 3 times 5
c A LaTex expression showing 1 over square root of 2 times 3 times 3 times 5
d A LaTex expression showing 1 over square root of 3 times 3 times 5 times 13
e A LaTex expression showing 1 over square root of 3 times 3 times 5 times 11
f A LaTex expression showing 1 over square root of 3 times 3 times 5 times 5
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 144 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3 times 3
c A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3 times 3
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 6 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 4 times 3 times 3
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 3
3
Factor this exponent's base number and express it as a radical
A LaTex expression showing 48 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 5
c A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 4 times 2 times 3
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 13
4
Factor this exponent's base number and express it as a radical
A LaTex expression showing 16 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2
c A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 2
d A LaTex expression showing 1 over square root of 2 times 2 times 4
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 7
f A LaTex expression showing 1 over square root of 2 times 4 times 2
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 72 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 2 times 2 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 9
c A LaTex expression showing 1 over square root of 2 times 4 times 3 times 3
d A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3 times 3
f A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 54 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 3 times 9
c A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3
d A LaTex expression showing 1 over square root of 2 times 3 times 3
e A LaTex expression showing 1 over square root of 2 times 9 times 3
f A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3 times 13
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 100 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 5 times 5
b A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5 times 7
c A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5
d A LaTex expression showing 1 over square root of 2 times 2 times 5
e A LaTex expression showing 1 over square root of 2 times 2 times 2 times 5 times 5
f A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5 times 11