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Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Radical (Level 1)

This math topic focuses on the skill of expressing non-square integer bases with fractional exponents as factored radicals. Students are challenged to factor a base number and then rewrite it under a radical, specifically utilizing the square root operation. The problems within the topic offer various integers for factorization, aiming to develop and reinforce students' understanding of the connection between exponents, factorization, and radicals. This exercise is part of an introductory unit on fractional bases and exponents, enhancing students' competency in manipulating 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

150(12)150^{(\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 1)'. Part of a broader unit on 'Exponents - Fractional Bases and Exponents - Intro' Learn online: app.mobius.academy/math/units/exponents_fractional_bases_and_exponents_intro/
1
Factor this exponent's base number and express it as a radical
A LaTex expression showing 54 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 9 times 3
b A LaTex expression showing square root of 2 times 3 times 3 times 3
c A LaTex expression showing square root of 2 times 3 times 3 times 3 times 3
d A LaTex expression showing square root of 2 times 2 times 3 times 3 times 3
e A LaTex expression showing square root of 3 times 3 times 3
f A LaTex expression showing square root of 2 times 3 times 3 times 3 times 5
2
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 times 5
b A LaTex expression showing square root of 2 times 3 times 3 times 5
c A LaTex expression showing square root of 3 times 3 times 5 times 7
d A LaTex expression showing square root of 3 times 3 times 3 times 5
e A LaTex expression showing square root of 3 times 3 times 5
f A LaTex expression showing square root of 3 times 3 times 5 times 11
3
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 times 2 times 3
c A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3
d A LaTex expression showing square root of 2 times 2 times 2 times 2
e A LaTex expression showing square root of 2 times 2 times 2 times 3
f A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3 times 3
4
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 2 times 9
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 2 times 3 times 3
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 3 times 3 times 13
f A LaTex expression showing square root of 2 times 2 times 3 times 3
5
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 2 times 3
b A LaTex expression showing square root of 2 times 2 times 3 times 11
c A LaTex expression showing square root of 2 times 2 times 3 times 7
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 2 times 3 times 5
f A LaTex expression showing square root of 2 times 2 times 3
6
Factor this exponent's base number and express it as a radical
A LaTex expression showing 32 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 4 times 2 times 2
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
d A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times 7
e A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times 13
f A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times 2
7
Factor this exponent's base number and express it as a radical
A LaTex expression showing 108 to the power of (1 over 2 )
a A LaTex expression showing square root of 2 times 2 times 3 times 3 times 3 times 5
b A LaTex expression showing square root of 2 times 2 times 3 times 9
c A LaTex expression showing square root of 2 times 2 times 3 times 3 times 3
d A LaTex expression showing square root of 2 times 2 times 3 times 3 times 3 times 13
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 times 3