Radicals - 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.

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

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Convert the fractional exponent to a radical

513r235^{\frac{1}{3}}\cdot {r}^{\frac{2}{3}}

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 Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Convert the fractional exponent to a radical
A LaTex expression showing 11 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 7{m to the power of 2 }
b A LaTex expression showing 3-th root of 13m
c A LaTex expression showing 3-th root of 10{m to the power of 4 }
d A LaTex expression showing 3-th root of 12m
e A LaTex expression showing 3-th root of 11{m to the power of 2 }
f A LaTex expression showing 3-th root of 13{m to the power of 3 }
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 2 over 3
a A LaTex expression showing 3-th root of 9z
b A LaTex expression showing 3-th root of 11{z to the power of 2 }
c A LaTex expression showing 3-th root of 12z
d A LaTex expression showing 33-th root of 13z
e A LaTex expression showing 3-th root of 9{z to the power of 4 }
f A LaTex expression showing 43-th root of 13{z to the power of 3 }
3
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 3 times p to the power of 1 over 3
a A LaTex expression showing 33-th root of {p to the power of 2 }
b A LaTex expression showing 43-th root of 8p
c A LaTex expression showing 3-th root of 6p
d A LaTex expression showing 3-th root of 5p
e A LaTex expression showing 3-th root of 2p
f A LaTex expression showing 3-th root of 7p
4
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of 1 over 3 times {c} to the power of 4 over 3
a A LaTex expression showing 3-th root of 3{c to the power of 4 }
b A LaTex expression showing 3{c} to the power of 3 3-th root of 3{c to the power of 3 }
c A LaTex expression showing 4c3-th root of 4{c to the power of 3 }
d A LaTex expression showing {c} to the power of 2 3-th root of 2{c to the power of 2 }
e A LaTex expression showing 4c3-th root of {c to the power of 3 }
f A LaTex expression showing {c} to the power of 3 3-th root of 3{c to the power of 3 }
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 33-th root of 10{x to the power of 2 }
b A LaTex expression showing 3-th root of 9x
c A LaTex expression showing 3-th root of 7x
d A LaTex expression showing 43-th root of 6{x to the power of 2 }
e A LaTex expression showing 3-th root of 8x
f A LaTex expression showing 3-th root of 9{x to the power of 2 }
6
Convert the fractional exponent to a radical
A LaTex expression showing 3 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 5{c to the power of 2 }
b A LaTex expression showing 43-th root of 5c
c A LaTex expression showing 3-th root of c
d A LaTex expression showing 3-th root of 3c
e A LaTex expression showing 33-th root of 2{c to the power of 2 }
f A LaTex expression showing 3-th root of 5c
7
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 1 over 3
a A LaTex expression showing 3-th root of 5{m to the power of 3 }
b A LaTex expression showing 3-th root of m
c A LaTex expression showing 3-th root of 2m
d A LaTex expression showing 33-th root of 3{m to the power of 3 }
e A LaTex expression showing 43-th root of 3m
f A LaTex expression showing 33-th root of 4{m to the power of 2 }