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Radicals - Convert Cube Root, Values and Variables, from Exponents - Positive (Level 2)

This math topic covers the conversion of fractional exponents into radical forms, specifically dealing with cube roots involving different values and variables. It emphasizes understanding and manipulating expressions with positive fractional exponents to transform them into equivalent radical expressions. The problems presented include multiple-choice answers for the students to select the correct radical form of given exponent expressions, further enhancing their skills in simplifying advanced radicals.

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

513â‹…n43â‹…b435^{\frac{1}{3}}\cdot {n}^{\frac{4}{3}}\cdot {b}^{\frac{4}{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 2)'. 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 11 to the power of 1 over 3 times {x} to the power of 2 over 3 times {z} to the power of 2 over 3
a A LaTex expression showing 3-th root of 13{x to the power of 2 {z} to the power of 4 }
b A LaTex expression showing 3-th root of 11{x to the power of 3 z}
c A LaTex expression showing 23-th root of 11x{z to the power of 4 }
d A LaTex expression showing 23-th root of 12x{z to the power of 4 }
e A LaTex expression showing 3-th root of 7x{z to the power of 3 }
f A LaTex expression showing 3-th root of 11{x to the power of 2 {z} to the power of 2 }
2
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 times {r} to the power of 5 over 3
a A LaTex expression showing r3-th root of 7dr
b A LaTex expression showing 3-th root of 5{d to the power of 2 {r} to the power of 5 }
c A LaTex expression showing 2{r} to the power of 2 3-th root of 8dr
d A LaTex expression showing {r} to the power of 2 3-th root of 5{d to the power of 4 r}
e A LaTex expression showing 2r3-th root of 2d{r to the power of 3 }
f A LaTex expression showing {r} to the power of 3 3-th root of 4{d to the power of 4 r}
3
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 times {n} to the power of 4 over 3
a A LaTex expression showing 3{m} to the power of 2 {n} to the power of 3 3-th root of mn
b A LaTex expression showing m{n} to the power of 2 3-th root of 6m{n to the power of 2 }
c A LaTex expression showing 3m{n} to the power of 2 3-th root of {m to the power of 3 n}
d A LaTex expression showing 3-th root of 3{m to the power of 4 {n} to the power of 4 }
e A LaTex expression showing m{n} to the power of 3 3-th root of 6mn
f A LaTex expression showing 3mn3-th root of {m to the power of 2 {n} to the power of 2 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 3 times {x} to the power of 4 over 3 times p to the power of 1 over 3
a A LaTex expression showing x3-th root of 11{x to the power of 2 p}
b A LaTex expression showing {x} to the power of 2 3-th root of 10xp
c A LaTex expression showing {x} to the power of 2 3-th root of 7{x to the power of 3 {p} to the power of 2 }
d A LaTex expression showing 3-th root of 11{x to the power of 4 p}
e A LaTex expression showing {x} to the power of 2 3-th root of 14x{p to the power of 2 }
f A LaTex expression showing {x} to the power of 2 3-th root of 9{x to the power of 2 {p} to the power of 3 }
5
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 4 over 3 times {n} to the power of 4 over 3
a A LaTex expression showing 4m{n} to the power of 2 3-th root of 8m{n to the power of 2 }
b A LaTex expression showing 3-th root of 11{m to the power of 4 {n} to the power of 4 }
c A LaTex expression showing {m} to the power of 3 n3-th root of 8{m to the power of 2 n}
d A LaTex expression showing 4mn3-th root of 11{m to the power of 2 {n} to the power of 2 }
e A LaTex expression showing 3{m} to the power of 2 {n} to the power of 3 3-th root of 10mn
f A LaTex expression showing {m} to the power of 3 {n} to the power of 3 3-th root of 12{m to the power of 2 n}
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times {n} to the power of 2 over 3 times {c} to the power of 2 over 3
a A LaTex expression showing 3-th root of 2{n to the power of 2 {c} to the power of 2 }
b A LaTex expression showing 3-th root of {n to the power of 2 c}
c A LaTex expression showing 3-th root of 2{n to the power of 2 c}
d A LaTex expression showing 3-th root of {n to the power of 4 {c} to the power of 4 }
e A LaTex expression showing 3-th root of 3{n to the power of 2 {c} to the power of 4 }
f A LaTex expression showing 3-th root of n{c to the power of 3 }
7
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 3 times p to the power of 1 over 3 times {n} to the power of 4 over 3
a A LaTex expression showing 3{n} to the power of 2 3-th root of {p to the power of 3 n}
b A LaTex expression showing n3-th root of 4pn
c A LaTex expression showing {n} to the power of 3 3-th root of 5pn
d A LaTex expression showing 3-th root of 2p{n to the power of 4 }
e A LaTex expression showing {n} to the power of 3 3-th root of {p to the power of 2 n}
f A LaTex expression showing n3-th root of pn