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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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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 2 to the power of 1 over 3 times z to the power of 1 over 3 times {c} to the power of 5 over 3
a A LaTex expression showing c3-th root of 5zc
b A LaTex expression showing 2c3-th root of {z to the power of 2 {c} to the power of 2 }
c A LaTex expression showing 1 over c3-th root of z{c to the power of 2 }
d A LaTex expression showing {c} to the power of 3 3-th root of zc
e A LaTex expression showing 3-th root of 2z{c to the power of 5 }
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times {m} to the power of 4 over 3 times {p} to the power of 2 over 3
a A LaTex expression showing 3-th root of 7{m to the power of 4 {p} to the power of 2 }
b A LaTex expression showing 1 over {m to the power of 2 3-th root of 10m{p to the power of 2 }}
c A LaTex expression showing 3m3-th root of 10{m to the power of 3 {p} to the power of 4 }
d A LaTex expression showing {m} to the power of 2 3-th root of 8m{p to the power of 2 }
e A LaTex expression showing {m} to the power of 3 3-th root of 3mp
3
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 3 times {c} to the power of 4 over 3 times {n} to the power of 4 over 3
a A LaTex expression showing 1 over {c to the power of 3 n3-th root of 9c{n to the power of 3 }}
b A LaTex expression showing {c} to the power of 3 {n} to the power of 2 3-th root of 12cn
c A LaTex expression showing 4{c} to the power of 3 {n} to the power of 3 3-th root of 14cn
d A LaTex expression showing 3-th root of 11{c to the power of 4 {n} to the power of 4 }
e A LaTex expression showing {c} to the power of 2 {n} to the power of 3 3-th root of 10c{n 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 {r} to the power of 2 over 3 times {x} to the power of 5 over 3
a A LaTex expression showing x3-th root of 2r{x to the power of 2 }
b A LaTex expression showing {x} to the power of 3 3-th root of 3{r to the power of 4 {x} to the power of 3 }
c A LaTex expression showing 1 over 4{x to the power of 3 3-th root of 4{r to the power of 3 x}}
d A LaTex expression showing 3-th root of 3{r to the power of 2 {x} to the power of 5 }
e A LaTex expression showing x3-th root of {r to the power of 4 {x} to the power of 4 }
5
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 times {b} to the power of 4 over 3
a A LaTex expression showing 1 over yb3-th root of {y to the power of 2b }
b A LaTex expression showing 3-th root of 2{y to the power of 4 {b} to the power of 4 }
c A LaTex expression showing y{b} to the power of 2 3-th root of 2{y to the power of 2 b}
d A LaTex expression showing 2{y} to the power of 2 b3-th root of yb
e A LaTex expression showing 4{y} to the power of 3 b3-th root of {y to the power of 2 b}
6
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 2 over 3 times {c} to the power of 5 over 3
a A LaTex expression showing 4c3-th root of 3{y to the power of 4 c}
b A LaTex expression showing 3c3-th root of {y to the power of 4 {c} to the power of 2 }
c A LaTex expression showing 3c3-th root of 5y{c to the power of 2 }
d A LaTex expression showing 3-th root of 2{y to the power of 2 {c} to the power of 5 }
e A LaTex expression showing 1 over 4c3-th root of {y to the power of 2{c to the power of 4 }}
7
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times {d} to the power of 5 over 3 times {r} to the power of 5 over 3
a A LaTex expression showing {d} to the power of 2 {r} to the power of 3 3-th root of 8{d to the power of 4 r}
b A LaTex expression showing 2dr3-th root of 10d{r to the power of 4 }
c A LaTex expression showing 3d{r} to the power of 2 3-th root of 5{d to the power of 4 r}
d A LaTex expression showing 3-th root of 7{d to the power of 5 {r} to the power of 5 }
e A LaTex expression showing 1 over d{r to the power of 2 3-th root of 8{d to the power of 4 {r} to the power of 4 }}
8
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 5 over 3 times {x} to the power of 2 over 3
a A LaTex expression showing m3-th root of 5{m to the power of 2 x}
b A LaTex expression showing {m} to the power of 3 3-th root of {m to the power of 4 x}
c A LaTex expression showing 3-th root of 3{m to the power of 5 {x} to the power of 2 }
d A LaTex expression showing 1 over 2m3-th root of 5m{x to the power of 3 }
e A LaTex expression showing 2m3-th root of 6{m to the power of 3 x}