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

This math topic focuses on understanding and solving problems related to negative fractional exponents with non-square integer bases, converting these expressions to simplified radicals. It encompasses multiple-choice questions where learners must evaluate various bases raised to fractional negative powers, requiring them to simplify the exponents to their radical forms. This involves critical thinking and a solid grasp of both radical and exponential expressions. This subject is a subset of a broader module on negative, fractional, and power laws of exponents, providing a deeper exploration of exponent manipulation and evaluation.

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 Simplified Radical

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


Find the answer when this number is raised to its exponent

54(−13)54^{(\frac{-1}{3})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Non-Square Integer Base - Exponent to Simplified 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
Find the answer when this number is raised to its exponent
A LaTex expression showing 50 to the power of (-1 over 2 )
a A LaTex expression showing 1 over 4square root of 2
b A LaTex expression showing 1 over 5square root of 2
c A LaTex expression showing 1 over 5
d A LaTex expression showing 1 over 5square root of 4
e A LaTex expression showing 1 over square root of 2
f A LaTex expression showing 1 over 3square root of 2
2
Find the answer when this number is raised to its exponent
A LaTex expression showing 144 to the power of (-1 over 2 )
a A LaTex expression showing 1 over 12square root of 3
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over 3
d A LaTex expression showing 1 over 12
e A LaTex expression showing 1 over 12square root of 4
f A LaTex expression showing 1 over 12square root of 2
3
Find the answer when this number is raised to its exponent
A LaTex expression showing 108 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 3
b A LaTex expression showing 1 over 6
c A LaTex expression showing 1 over 4square root of 3
d A LaTex expression showing 1 over 2square root of 3
e A LaTex expression showing 1 over 6square root of 3
f A LaTex expression showing 1 over 5square root of 3
4
Find the answer when this number is raised to its exponent
A LaTex expression showing 250 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 23-th root of 2
b A LaTex expression showing 1 over 43-th root of 2
c A LaTex expression showing 1 over 5
d A LaTex expression showing 1 over 3-th root of 2
e A LaTex expression showing 1 over 53-th root of 4
f A LaTex expression showing 1 over 53-th root of 2
5
Find the answer when this number is raised to its exponent
A LaTex expression showing 32 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 23-th root of 3
b A LaTex expression showing 1 over 53-th root of 4
c A LaTex expression showing 1 over 23-th root of 4
d A LaTex expression showing 1 over 2
e A LaTex expression showing 1 over 43-th root of 4
f A LaTex expression showing 1 over 3-th root of 4
6
Find the answer when this number is raised to its exponent
A LaTex expression showing 128 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 4
b A LaTex expression showing 1 over 3-th root of 2
c A LaTex expression showing 1 over 53-th root of 2
d A LaTex expression showing 1 over 43-th root of 2
7
Find the answer when this number is raised to its exponent
A LaTex expression showing 48 to the power of (-1 over 2 )
a A LaTex expression showing 1 over 4square root of 2
b A LaTex expression showing 1 over 2square root of 3
c A LaTex expression showing 1 over 4
d A LaTex expression showing 1 over square root of 3
e A LaTex expression showing 1 over 5square root of 3
f A LaTex expression showing 1 over 4square root of 3