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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Radicals - Convert Cube Root, Values and Variables, from Exponents - Positive
1
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 1 over 23-th root of 8{n to the power of 3 }
c A LaTex expression showing 3-th root of 11{n to the power of 2 }
d A LaTex expression showing 33-th root of 9n
e A LaTex expression showing 33-th root of 11n
2
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times {m} to the power of 2 over 3
a A LaTex expression showing 3-th root of 3m
b A LaTex expression showing 33-th root of {m to the power of 4 }
c A LaTex expression showing 1 over 33-th root of m
d A LaTex expression showing 3-th root of 2m
e A LaTex expression showing 3-th root of 2{m to the power of 2 }
3
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 4 over 3
a A LaTex expression showing 3-th root of 11{z to the power of 4 }
b A LaTex expression showing {z} to the power of 2 3-th root of 7z
c A LaTex expression showing 4{z} to the power of 2 3-th root of 8{z to the power of 2 }
d A LaTex expression showing 3z3-th root of 13{z to the power of 2 }
e A LaTex expression showing 1 over 2z3-th root of 14{z to the power of 2 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of 1 over 3 times {m} to the power of 2 over 3
a A LaTex expression showing 3-th root of 3{m to the power of 2 }
b A LaTex expression showing 23-th root of 3{m to the power of 2 }
c A LaTex expression showing 3-th root of 5{m to the power of 3 }
d A LaTex expression showing 33-th root of 2{m to the power of 2 }
e A LaTex expression showing 1 over 33-th root of {m to the power of 4 }
5
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 3 times {d} to the power of 2 over 3
a A LaTex expression showing 3-th root of 5{d to the power of 2 }
b A LaTex expression showing 3-th root of 4{d to the power of 3 }
c A LaTex expression showing 3-th root of 4{d to the power of 2 }
d A LaTex expression showing 1 over 3-th root of 7d
e A LaTex expression showing 3-th root of 7d
6
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of 1 over 3 times {b} to the power of 2 over 3
a A LaTex expression showing 3-th root of {b to the power of 4 }
b A LaTex expression showing 1 over 3-th root of {b to the power of 2 }
c A LaTex expression showing 3-th root of 3{b to the power of 2 }
d A LaTex expression showing 3-th root of b
e A LaTex expression showing 33-th root of {b to the power of 3 }
7
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 1 over 3-th root of 3{c to the power of 2 }
b A LaTex expression showing 1 over 23-th root of 3c
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 43-th root of 4c
8
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times p to the power of 1 over 3
a A LaTex expression showing 3-th root of 7p
b A LaTex expression showing 1 over 3-th root of 7p
c A LaTex expression showing 1 over 3-th root of 8p
d A LaTex expression showing 3-th root of 9p
e A LaTex expression showing 33-th root of 3p