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Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical (Level 2)

This math topic focuses on the practice of simplifying negative fractional exponents with non-square integer bases into radical expressions with factored bases. The problems involve converting expressions like those raised to the power of \(-\frac{1}{2}\) or \(-\frac{1}{3}\) into their radical counterparts, making sure to factorize the base correctly and then express them in radical form. It includes multiple choices for each expression, allowing users to select the correct factorization and radical representation. The topic falls under a broader unit of negative bases and exponents practice.

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

45(−12)45^{(\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 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 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 3 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 3
c A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3 times 13
d A LaTex expression showing 1 over square root of 2 times 9 times 3
e A LaTex expression showing 1 over square root of 2 times 3 times 9
f A LaTex expression showing 1 over square root of 2 times 3 times 3 times 3
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 12 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3
b A LaTex expression showing 1 over square root of 2 times 2 times 2 times 3
c A LaTex expression showing 1 over square root of 2 times 2 times 3 times 5
d A LaTex expression showing 1 over square root of 2 times 2 times 3
e A LaTex expression showing 1 over square root of 2 times 2 times 3 times 13
f A LaTex expression showing 1 over square root of 2 times 2 times 3 times 11
3
Factor this exponent's base number and express it as a radical
A LaTex expression showing 180 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 2 times 6 times 3 times 5
b A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3
c A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5 times 11
d A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5 times 5
e A LaTex expression showing 1 over square root of 2 times 2 times 3 times 3 times 5
f A LaTex expression showing 1 over square root of 2 times 2 times 3 times 15
4
Factor this exponent's base number and express it as a radical
A LaTex expression showing 162 to the power of (-1 over 4 )
a A LaTex expression showing 1 over 4-th root of 2 times 3 times 3 times 9
b A LaTex expression showing 1 over 4-th root of 2 times 3 times 3 times 3
c A LaTex expression showing 1 over 4-th root of 2 times 2 times 3 times 3 times 3 times 3
d A LaTex expression showing 1 over 4-th root of 2 times 3 times 3 times 3 times 3 times 5
e A LaTex expression showing 1 over 4-th root of 2 times 9 times 3 times 3
f A LaTex expression showing 1 over 4-th root of 2 times 3 times 3 times 3 times 3
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 162 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3-th root of 2 times 3 times 3 times 3 times 3
b A LaTex expression showing 1 over 3-th root of 2 times 3 times 3 times 3 times 3 times 5
c A LaTex expression showing 1 over 3-th root of 2 times 9 times 3 times 3
d A LaTex expression showing 1 over 3-th root of 2 times 3 times 3 times 3
e A LaTex expression showing 1 over 3-th root of 2 times 3 times 3 times 9
f A LaTex expression showing 1 over 3-th root of 2 times 2 times 3 times 3 times 3 times 3
6
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
d A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5
e A LaTex expression showing 1 over square root of 2 times 2 times 5 times 5 times 11
f A LaTex expression showing 1 over square root of 2 times 2 times 2 times 5 times 5
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 192 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 2 times 2 times 2 times 3
b A LaTex expression showing 1 over 3-th root of 2 times 4 times 2 times 2 times 2 times 3
c A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 2 times 2 times 2 times 3 times 7
d A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 2 times 2 times 6
e A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 2 times 2 times 2 times 2 times 3
f A LaTex expression showing 1 over 3-th root of 2 times 2 times 2 times 4 times 2 times 3