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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.

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

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

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Convert the fractional exponent to a radical

313â‹…c133^{\frac{1}{3}}\cdot c^{\frac{1}{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 3 to the power of 1 over 3 times {c} to the power of 4 over 3
a A LaTex expression showing {c} to the power of 2 3-th root of 2{c to the power of 2 }
b A LaTex expression showing 4c3-th root of 4{c to the power of 3 }
c A LaTex expression showing {c} to the power of 3 3-th root of 3{c to the power of 3 }
d A LaTex expression showing 4c3-th root of {c to the power of 3 }
e A LaTex expression showing 3-th root of 3{c to the power of 4 }
f A LaTex expression showing 3{c} to the power of 3 3-th root of 3{c to the power of 3 }
2
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times {c} to the power of 4 over 3
a A LaTex expression showing 3c3-th root of 5c
b A LaTex expression showing {c} to the power of 3 3-th root of 2c
c A LaTex expression showing 3-th root of 2{c to the power of 4 }
d A LaTex expression showing {c} to the power of 3 3-th root of c
e A LaTex expression showing c3-th root of c
f A LaTex expression showing {c} to the power of 2 3-th root of c
3
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times {y} to the power of 4 over 3
a A LaTex expression showing {y} to the power of 2 3-th root of {y to the power of 2 }
b A LaTex expression showing {y} to the power of 3 3-th root of y
c A LaTex expression showing 2y3-th root of 4y
d A LaTex expression showing 3-th root of 2{y to the power of 4 }
e A LaTex expression showing 2{y} to the power of 2 3-th root of y
f A LaTex expression showing y3-th root of 4{y to the power of 2 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 3 times n to the power of 1 over 3
a A LaTex expression showing 3-th root of 3n
b A LaTex expression showing 33-th root of 8n
c A LaTex expression showing 3-th root of 5n
d A LaTex expression showing 23-th root of 5n
e A LaTex expression showing 3-th root of 8n
f A LaTex expression showing 33-th root of 5n
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 7x
b A LaTex expression showing 43-th root of 6{x to the power of 2 }
c A LaTex expression showing 3-th root of 8x
d A LaTex expression showing 3-th root of 9{x to the power of 2 }
e A LaTex expression showing 33-th root of 10{x to the power of 2 }
f A LaTex expression showing 3-th root of 9x
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times d to the power of 1 over 3
a A LaTex expression showing 33-th root of 2{d to the power of 3 }
b A LaTex expression showing 3-th root of d
c A LaTex expression showing 43-th root of d
d A LaTex expression showing 33-th root of d
e A LaTex expression showing 43-th root of 3d
f A LaTex expression showing 3-th root of 2d
7
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 4 over 3
a A LaTex expression showing 3-th root of 3{m to the power of 4 }
b A LaTex expression showing 2m3-th root of m
c A LaTex expression showing {m} to the power of 3 3-th root of {m to the power of 3 }
d A LaTex expression showing {m} to the power of 3 3-th root of {m to the power of 2 }
e A LaTex expression showing m3-th root of m
f A LaTex expression showing {m} to the power of 3 3-th root of 5{m to the power of 3 }