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

This math topic focuses on calculating fractional exponents for non-square integer bases and converting the outcome into simplified radicals. Specific skills practiced include understanding and applying fractional exponents (like 1/2, 1/3) to integer bases (such as 20, 100, 192) and interpreting these expressions as radicals like square roots and cube roots. Problems require evaluating these expressions and choosing the correct simplified form from multiple answer choices. This falls under a broader study of negative, fractional exponents, and power laws.

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

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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

100(12)100^{(\frac{1}{2})}

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

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Math worksheet on 'Exponents - 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 16 to the power of (1 over 2 )
a A LaTex expression showing 4square root of 3
b A LaTex expression showing 4square root of 4
c A LaTex expression showing 5
d A LaTex expression showing 1
e A LaTex expression showing 4square root of 2
f A LaTex expression showing 4
2
Find the answer when this number is raised to its exponent
A LaTex expression showing 24 to the power of (1 over 2 )
a A LaTex expression showing 5square root of 6
b A LaTex expression showing 2
c A LaTex expression showing 2square root of 3
d A LaTex expression showing square root of 6
e A LaTex expression showing 2square root of 2
f A LaTex expression showing 2square root of 6
3
Find the answer when this number is raised to its exponent
A LaTex expression showing 108 to the power of (1 over 3 )
a A LaTex expression showing 23-th root of 4
b A LaTex expression showing 3-th root of 4
c A LaTex expression showing 33-th root of 3
d A LaTex expression showing 3
e A LaTex expression showing 33-th root of 2
f A LaTex expression showing 33-th root of 4
4
Find the answer when this number is raised to its exponent
A LaTex expression showing 75 to the power of (1 over 2 )
a A LaTex expression showing 3square root of 3
b A LaTex expression showing 5square root of 3
c A LaTex expression showing 4square root of 3
d A LaTex expression showing 5
e A LaTex expression showing square root of 3
f A LaTex expression showing 5square root of 4
5
Find the answer when this number is raised to its exponent
A LaTex expression showing 48 to the power of (1 over 4 )
a A LaTex expression showing 44-th root of 3
b A LaTex expression showing 4-th root of 3
c A LaTex expression showing 34-th root of 3
d A LaTex expression showing 24-th root of 3
e A LaTex expression showing 2
f A LaTex expression showing 54-th root of 3
6
Find the answer when this number is raised to its exponent
A LaTex expression showing 32 to the power of (1 over 2 )
a A LaTex expression showing 4square root of 2
b A LaTex expression showing 4square root of 4
c A LaTex expression showing square root of 2
d A LaTex expression showing 5square root of 2
e A LaTex expression showing 2square root of 2
f A LaTex expression showing 4
7
Find the answer when this number is raised to its exponent
A LaTex expression showing 72 to the power of (1 over 2 )
a A LaTex expression showing square root of 2
b A LaTex expression showing 6square root of 2
c A LaTex expression showing 2square root of 2
d A LaTex expression showing 6square root of 4
e A LaTex expression showing 6square root of 3
f A LaTex expression showing 6