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

This math topic focuses on converting fractional exponents with square integer bases into their equivalent radical forms. The problems challenge students to identify the correct radical expression equivalent to given powers, such as finding the square root, fourth root, or cube root corresponding to various fractional exponent forms of integers like 25, 16, 4, 125, 81, 8, and 16. Each question offers multiple-choice answers, requiring learners to select the correct radical transformation of the given exponentiation expression. This skill is foundational for understanding properties of exponents and radicals in algebra.

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

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

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Exponents - Fractional Exponents with Square Integer Base - Exponent to Radical
1
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 3-th root of 216
b A LaTex expression showing 53-th root of 216
c A LaTex expression showing 23-th root of 216
d A LaTex expression showing 1 over 3-th root of 216
e A LaTex expression showing 1
f A LaTex expression showing 33-th root of 216
2
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 81 to the power of (1 over 4 )
a A LaTex expression showing 1 over 4-th root of 81
b A LaTex expression showing 4-th root of 81 to the power of 4
c A LaTex expression showing 24-th root of 81
d A LaTex expression showing 1
e A LaTex expression showing 4-th root of 81
3
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 3square root of 9
b A LaTex expression showing square root of 4
c A LaTex expression showing square root of 9
d A LaTex expression showing 1
e A LaTex expression showing 2square root of 9
f A LaTex expression showing 4square root of 9
4
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 53-th root of 125
b A LaTex expression showing 23-th root of 125
c A LaTex expression showing 33-th root of 125
d A LaTex expression showing 1
e A LaTex expression showing 43-th root of 125
f A LaTex expression showing 3-th root of 125
5
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 square root of 16
b A LaTex expression showing 4square root of 16
c A LaTex expression showing 1
d A LaTex expression showing 2square root of 16
e A LaTex expression showing square root of 2
f A LaTex expression showing 3square root of 16
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 35-th root of 32
b A LaTex expression showing 45-th root of 32
c A LaTex expression showing 55-th root of 32
d A LaTex expression showing 1
e A LaTex expression showing 5-th root of 32
f A LaTex expression showing 25-th root of 32
7
Find the radical that is the same as this number raised to its exponent
A LaTex expression showing 4 to the power of (1 over 2 )
a A LaTex expression showing 4square root of 4
b A LaTex expression showing 2square root of 4
c A LaTex expression showing square root of 3
d A LaTex expression showing square root of 4
e A LaTex expression showing 3square root of 4
f A LaTex expression showing 1
8
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 24-th root of 16
b A LaTex expression showing 1
c A LaTex expression showing 4-th root of 16
d A LaTex expression showing 1 over 4-th root of 16
e A LaTex expression showing 4-th root of 16 to the power of 4
f A LaTex expression showing 54-th root of 16