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Radical

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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Convert the fractional exponent to a radical

713⋅y53⋅r437^{\frac{1}{3}}\cdot {y}^{\frac{5}{3}}\cdot {r}^{\frac{4}{3}}

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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 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 {d} to the power of 2 over 3 times {p} to the power of 4 over 3
a A LaTex expression showing 3-th root of 11{d to the power of 2 {p} to the power of 4 }
b A LaTex expression showing {p} to the power of 3 3-th root of 8d{p to the power of 3 }
c A LaTex expression showing p3-th root of 14{d to the power of 4 p}
d A LaTex expression showing p3-th root of 7{d to the power of 4 p}
e A LaTex expression showing p3-th root of 13dp
f A LaTex expression showing p3-th root of 14{d to the power of 2 p}
2
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 5 over 3 times {z} to the power of 4 over 3
a A LaTex expression showing 4bz3-th root of 5{b to the power of 2 {z} to the power of 3 }
b A LaTex expression showing 3-th root of 3{b to the power of 5 {z} to the power of 4 }
c A LaTex expression showing {b} to the power of 3 {z} to the power of 3 3-th root of {b to the power of 2 {z} to the power of 2 }
d A LaTex expression showing b{z} to the power of 2 3-th root of {b to the power of 4 {z} to the power of 3 }
e A LaTex expression showing {b} to the power of 3 z3-th root of 3{b to the power of 2 z}
f A LaTex expression showing 2{b} to the power of 2 {z} to the power of 3 3-th root of b{z to the power of 2 }
3
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 4 over 3 times {p} to the power of 5 over 3
a A LaTex expression showing {d} to the power of 3 p3-th root of 5dp
b A LaTex expression showing dp3-th root of 6d{p to the power of 2 }
c A LaTex expression showing {d} to the power of 3 p3-th root of 5{d to the power of 3 p}
d A LaTex expression showing {d} to the power of 2 {p} to the power of 3 3-th root of 8{d to the power of 2 p}
e A LaTex expression showing 3-th root of 5{d to the power of 4 {p} to the power of 5 }
f A LaTex expression showing 4{d} to the power of 2 p3-th root of 5d{p to the power of 4 }
4
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 5 over 3 times {y} to the power of 5 over 3
a A LaTex expression showing c{y} to the power of 3 3-th root of 5{c to the power of 4 {y} to the power of 4 }
b A LaTex expression showing cy3-th root of 3{c to the power of 3 {y} to the power of 4 }
c A LaTex expression showing 3-th root of 7{c to the power of 5 {y} to the power of 5 }
d A LaTex expression showing c{y} to the power of 3 3-th root of 3c{y to the power of 2 }
e A LaTex expression showing 4{c} to the power of 2 y3-th root of 6c{y to the power of 3 }
f A LaTex expression showing 3{c} to the power of 2 {y} to the power of 2 3-th root of 10c{y to the power of 2 }
5
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 {b} to the power of 2 over 3
a A LaTex expression showing 2m3-th root of m{b to the power of 2 }
b A LaTex expression showing 4{m} to the power of 2 3-th root of m{b to the power of 3 }
c A LaTex expression showing 3-th root of 3{m to the power of 4 {b} to the power of 2 }
d A LaTex expression showing 2m3-th root of mb
e A LaTex expression showing m3-th root of 2{m to the power of 3 {b} to the power of 3 }
f A LaTex expression showing 2{m} to the power of 2 3-th root of 4mb
6
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 4mn3-th root of 11{m to the power of 2 {n} to the power of 2 }
b 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}
c A LaTex expression showing 3-th root of 11{m to the power of 4 {n} to the power of 4 }
d A LaTex expression showing 4m{n} to the power of 2 3-th root of 8m{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 n3-th root of 8{m to the power of 2 n}
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 {p to the power of 2 n}
d A LaTex expression showing 3-th root of 2p{n to the power of 4 }
e A LaTex expression showing n3-th root of pn
f A LaTex expression showing {n} to the power of 3 3-th root of 5pn