Convert Cube Root, Values and Variables, from Exponents - Positive (Level 1)

This math topic focuses on converting fractional exponents into radicals, specifically dealing with cube roots involving both values and variables. It is designed for introductory level practice under the broader unit of simplifying radicals. Each problem presents an expression with numbers and variables raised to fractional powers, followed by multiple-choice answers that feature different forms of radical expressions. Students are required to recognize and accurately convert these exponents into the appropriate radical form, strengthening their understanding of exponent and radical relationships.

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

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Radicals - Convert Cube Root, Values and Variables, from Exponents - Positive Worksheet

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Math worksheet on 'Radicals - Convert Cube Root, Values and Variables, from Exponents - Positive (Level 1)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 3 times c to the power of 1 over 3
a A LaTex expression showing 43-th root of 4c
b A LaTex expression showing 1 over 3-th root of 3{c to the power of 2 }
c A LaTex expression showing 3-th root of 5c
d A LaTex expression showing 33-th root of c
e A LaTex expression showing 1 over 23-th root of 3c
2
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 3 times z to the power of 1 over 3
a A LaTex expression showing 23-th root of 10z
b A LaTex expression showing 3-th root of 7{z to the power of 3 }
c A LaTex expression showing 3-th root of 12{z to the power of 2 }
d A LaTex expression showing 3-th root of 11z
e A LaTex expression showing 1 over 23-th root of 13z
3
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 3 times {c} to the power of 4 over 3
a A LaTex expression showing 1 over c3-th root of 8c
b A LaTex expression showing 3-th root of 5{c to the power of 4 }
c A LaTex expression showing 3{c} to the power of 2 3-th root of 6c
d A LaTex expression showing 4c3-th root of 6c
e A LaTex expression showing 4c3-th root of 7c
4
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 3 times {n} to the power of 2 over 3
a A LaTex expression showing 3-th root of 11{n to the power of 4 }
b A LaTex expression showing 3-th root of 11{n to the power of 2 }
c A LaTex expression showing 33-th root of 9n
d A LaTex expression showing 1 over 23-th root of 8{n to the power of 3 }
e A LaTex expression showing 33-th root of 11n
5
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times x to the power of 1 over 3
a A LaTex expression showing 3-th root of 9x
b A LaTex expression showing 3-th root of 10{x to the power of 2 }
c A LaTex expression showing 1 over 3-th root of 6x
d A LaTex expression showing 3-th root of 5x
e A LaTex expression showing 3-th root of 7x
6
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of 1 over 3 times {p} to the power of 4 over 3
a A LaTex expression showing 1 over 4p3-th root of 5p
b A LaTex expression showing {p} to the power of 3 3-th root of {p to the power of 3 }
c A LaTex expression showing p3-th root of {p to the power of 3 }
d A LaTex expression showing p3-th root of 4p
e A LaTex expression showing 3-th root of 3{p to the power of 4 }
7
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times c to the power of 1 over 3
a A LaTex expression showing 23-th root of 6{c to the power of 2 }
b A LaTex expression showing 1 over 3-th root of 10c
c A LaTex expression showing 33-th root of 7c
d A LaTex expression showing 3-th root of 7c
e A LaTex expression showing 1 over 33-th root of 5c