Exponent

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

This math topic focuses on converting negative fractional exponents with square integer bases into their radical equivalents. Each problem presents a number raised to a negative fractional exponent and asks to identify the equivalent radical form among multiple choices. The exponents explored are typically in the forms of -1/2, -1/3, -1/4, and -1/5, applied to integer bases like 16, 25, 32, etc. Multiple-choice answers include various radical transformations and instructional mistakes to test understanding and application skills related to roots and their properties.

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 Radical

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


Find the radical that is the same as this number raised to its exponent

125(13)125^{(\frac{-1}{3})}

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

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Math worksheet on 'Exponents - Negative Fractional Exponents with Square Integer Base - Exponent to Radical (Level 2)'. Part of a broader unit on 'Exponents - Fractional Bases and Exponents - Practice' Learn online: app.mobius.academy/math/units/exponents_fractional_bases_and_exponents_practice/
1
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 125 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 43-th root of 125
b A LaTex expression showing 1 over 3-th root of 125
c A LaTex expression showing 1 over 3-th root of 125 to the power of 2
d A LaTex expression showing 3-th root of 125 to the power of 3
e A LaTex expression showing 3-th root of 125
f A LaTex expression showing 1 over 1
2
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 9 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 9
b A LaTex expression showing 1 over 4square root of 9
c A LaTex expression showing 1 over 3square root of 9
d A LaTex expression showing 1 over 5square root of 9
e A LaTex expression showing 1 over 1
f A LaTex expression showing 1 over square root of 9 to the power of 2
3
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 27 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 43-th root of 27
b A LaTex expression showing 1 over 3-th root of 3
c A LaTex expression showing 1 over 3-th root of 2
d A LaTex expression showing 1 over 3-th root of 27
e A LaTex expression showing 1 over 53-th root of 27
f A LaTex expression showing 1 over 1
4
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 16 to the power of (-1 over 4 )
a A LaTex expression showing 1 over 1
b A LaTex expression showing 1 over 34-th root of 16
c A LaTex expression showing 1 over 4-th root of 2
d A LaTex expression showing 1 over 24-th root of 16
e A LaTex expression showing 1 over 4-th root of 16
f A LaTex expression showing 1 over 44-th root of 16
5
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 216 to the power of (-1 over 3 )
a A LaTex expression showing 1 over 3-th root of 216 to the power of 2
b A LaTex expression showing 1 over 1
c A LaTex expression showing 1 over 23-th root of 216
d A LaTex expression showing 1 over 53-th root of 216
e A LaTex expression showing 1 over 3-th root of 216
f A LaTex expression showing 3-th root of 216
6
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 32 to the power of (-1 over 5 )
a A LaTex expression showing 1 over 5-th root of 32
b A LaTex expression showing 1 over 5-th root of 32 to the power of 2
c A LaTex expression showing 1 over 25-th root of 32
d A LaTex expression showing 5-th root of 32
e A LaTex expression showing 1 over 1
f A LaTex expression showing 1 over 5-th root of 4
7
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 16 to the power of (-1 over 2 )
a A LaTex expression showing 1 over square root of 16 to the power of 2
b A LaTex expression showing square root of 16
c A LaTex expression showing 1 over 1
d A LaTex expression showing 1 over 5square root of 16
e A LaTex expression showing 1 over 3square root of 16
f A LaTex expression showing 1 over square root of 16