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

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

Factor this exponent's base number and express it as a radical

16(12)16^{(\frac{1}{2})}

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

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Math worksheet on 'Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored 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
Factor this exponent's base number and express it as a radical
A LaTex expression showing 72 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 2 times 3 times 3
b A LaTex expression showing square root of 2 times 2 times 2 times 3 times 3
c A LaTex expression showing square root of 2 times 2 times 2 times 3 times 3 times 13
d A LaTex expression showing square root of 2 times 2 times 6 times 3
e A LaTex expression showing square root of 2 times 2 times 2 times 9
f A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3 times 3
2
Factor this exponent's base number and express it as a radical
A LaTex expression showing 50 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 5 times 5 times 13
b A LaTex expression showing square root of 2 times 5 times 5 times 11
c A LaTex expression showing square root of 2 times 2 times 5 times 5
d A LaTex expression showing square root of 2 times 5 times 5 times 7
e A LaTex expression showing square root of 2 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 100 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 10 times 5
b A LaTex expression showing square root of 2 times 2 times 3 times 5 times 5
c A LaTex expression showing square root of 2 times 2 times 2 times 5 times 5
d A LaTex expression showing square root of 2 times 2 times 5 times 5 times 7
e A LaTex expression showing square root of 2 times 2 times 5 times 5
f A LaTex expression showing square root of 2 times 2 times 25
4
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 4 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 2 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
5
Factor this exponent's base number and express it as a radical
A LaTex expression showing 180 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 2 times 2 times 3 times 3 times 5
b A LaTex expression showing square root of 2 times 6 times 3 times 5
c A LaTex expression showing square root of 2 times 2 times 3 times 5
d A LaTex expression showing square root of 2 times 2 times 3 times 3
e A LaTex expression showing square root of 2 times 3 times 3 times 5
f A LaTex expression showing square root of 2 times 2 times 3 times 3 times 5
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 36 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 6 times 3
b A LaTex expression showing square root of 2 times 2 times 3 times 3 times 7
c A LaTex expression showing square root of 2 times 2 times 3 times 3 times 11
d A LaTex expression showing square root of 2 times 3 times 3
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 2 times 9
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 48 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 4 times 2 times 3
b A LaTex expression showing square root of 2 times 2 times 2 times 2
c A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times 3
d A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3
e A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3 times 3
f A LaTex expression showing square root of 2 times 2 times 2 times 3