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

This math topic focuses on the skill of expressing non-square integer bases with fractional exponents as factored radicals. It covers both square root and cube root cases. Problems involve factoring the base number of an expression, then writing the expression in radical form. The examples given include integers elevated to fractional powers, and students are required to choose the correct factored radical form among multiple options. This set of exercises emphasizes the understanding of fractional exponents and their relationship with radicals, enhancing fluency in managing expressions involving powers and roots.

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

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

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Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical
1
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 square root of 2 times 2 times 3 times 7
b A LaTex expression showing square root of 2 times 2 times 3 times 5
c A LaTex expression showing square root of 2 times 2 times 2 times 3
d A LaTex expression showing square root of 2 times 2 times 3
e A LaTex expression showing square root of 2 times 2 times 3 times 11
f A LaTex expression showing square root of 2 times 2 times 3 times 3
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 75 to the power of (1 over 2 )
a A LaTex expression showing square root of 3 times 5 times 5
b A LaTex expression showing square root of 3 times 5 times 5 times 7
c A LaTex expression showing square root of 3 times 5 times 5 times 13
d A LaTex expression showing square root of 3 times 5 times 5 times 11
e A LaTex expression showing square root of 3 times 3 times 5 times 5
f A LaTex expression showing square root of 2 times 3 times 5 times 5
3
Factor this exponent's base number and express it as a radical
A LaTex expression showing 16 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2
b A LaTex expression showing square root of 2 times 2 times 2
c A LaTex expression showing square root of 2 times 2 times 4
d A LaTex expression showing square root of 2 times 4 times 2
e A LaTex expression showing square root of 2 times 2 times 2 times 2 times 7
f A LaTex expression showing square root of 2 times 2 times 2 times 2
4
Factor this exponent's base number and express it as a radical
A LaTex expression showing 18 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 3 times 3 times 3
b A LaTex expression showing square root of 2 times 3 times 3 times 5
c A LaTex expression showing square root of 2 times 3 times 3 times 11
d A LaTex expression showing square root of 2 times 3 times 3 times 7
e A LaTex expression showing square root of 2 times 2 times 3 times 3
f A LaTex expression showing square root of 2 times 3 times 3
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 48 to the power of (1 over 4 )
a A LaTex expression showing 4-th root of 2 times 4 times 2 times 3
b A LaTex expression showing 4-th root of 2 times 2 times 2 times 3
c A LaTex expression showing 4-th root of 2 times 2 times 4 times 3
d A LaTex expression showing 4-th root of 2 times 2 times 2 times 6
e A LaTex expression showing 4-th root of 2 times 2 times 2 times 2 times 3
f A LaTex expression showing 4-th root of 2 times 2 times 2 times 2 times 3 times 13
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 108 to the power of (1 over 3 )
a A LaTex expression showing 3-th root of 2 times 2 times 2 times 3 times 3 times 3
b A LaTex expression showing 3-th root of 2 times 2 times 3 times 3 times 3 times 5
c A LaTex expression showing 3-th root of 2 times 2 times 3 times 3 times 3
d A LaTex expression showing 3-th root of 2 times 2 times 3 times 3
e A LaTex expression showing 3-th root of 2 times 2 times 9 times 3
f A LaTex expression showing 3-th root of 2 times 2 times 3 times 9
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 20 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 2 times 2 times 5
b A LaTex expression showing square root of 2 times 2 times 3 times 5
c A LaTex expression showing square root of 2 times 2 times 5
d A LaTex expression showing square root of 2 times 2 times 5 times 13
e A LaTex expression showing square root of 2 times 2 times 5 times 7
f A LaTex expression showing square root of 2 times 2 times 5 times 11
8
Factor this exponent's base number and express it as a radical
A LaTex expression showing 45 to the power of (1 over 2 )
a A LaTex expression showing square root of 3 times 3 times 5
b A LaTex expression showing square root of 3 times 3 times 5 times 11
c A LaTex expression showing square root of 2 times 3 times 3 times 5
d A LaTex expression showing square root of 3 times 3 times 5 times 5
e A LaTex expression showing square root of 3 times 3 times 3 times 5
f A LaTex expression showing square root of 3 times 3 times 5 times 7