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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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 3 to the power of 1 over 3 times b to the power of 1 over 3 times {m} to the power of 2 over 3
a A LaTex expression showing 1 over 3-th root of bm
b A LaTex expression showing 3-th root of b{m to the power of 4 }
c A LaTex expression showing 3-th root of 3{b to the power of 2 {m} to the power of 4 }
d A LaTex expression showing 3-th root of 3b{m to the power of 2 }
e A LaTex expression showing 3-th root of 2b{m to the power of 2 }
2
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 2dr3-th root of 10d{r to the power of 4 }
b 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 }}
c A LaTex expression showing 3-th root of 7{d to the power of 5 {r} to the power of 5 }
d A LaTex expression showing 3d{r} to the power of 2 3-th root of 5{d to the power of 4 r}
e 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}
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 {b} to the power of 4 over 3
a A LaTex expression showing 2{m} to the power of 3 b3-th root of 4mb
b A LaTex expression showing m{b} to the power of 3 3-th root of mb
c A LaTex expression showing 1 over 2{m to the power of 2 b3-th root of {m to the power of 2 b}}
d A LaTex expression showing 3-th root of 3{m to the power of 4 {b} to the power of 4 }
e A LaTex expression showing m{b} to the power of 3 3-th root of 2m{b to the power of 3 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 3 times {b} to the power of 5 over 3 times {p} to the power of 4 over 3
a A LaTex expression showing 4{b} to the power of 3 p3-th root of 5{b to the power of 3 {p} to the power of 3 }
b A LaTex expression showing 2b{p} to the power of 2 3-th root of 4{b to the power of 2 p}
c A LaTex expression showing {b} to the power of 3 p3-th root of 6{b to the power of 4 p}
d A LaTex expression showing 3-th root of 7{b to the power of 5 {p} to the power of 4 }
e A LaTex expression showing 1 over 3b{p to the power of 3 3-th root of 6{b to the power of 3 {p} 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 {x} to the power of 4 over 3 times {n} to the power of 5 over 3
a A LaTex expression showing 1 over 2{x to the power of 2 n3-th root of 3{x to the power of 3 n}}
b A LaTex expression showing 3-th root of 3{x to the power of 4 {n} to the power of 5 }
c A LaTex expression showing x{n} to the power of 3 3-th root of x{n to the power of 2 }
d A LaTex expression showing xn3-th root of 6x{n to the power of 3 }
e A LaTex expression showing xn3-th root of xn
6
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 3-th root of 3{m to the power of 5 {x} to the power of 2 }
c A LaTex expression showing 2m3-th root of 6{m to the power of 3 x}
d A LaTex expression showing 1 over 2m3-th root of 5m{x to the power of 3 }
e A LaTex expression showing {m} to the power of 3 3-th root of {m to the power of 4 x}
7
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 1 over 3 times y to the power of 1 over 3
a A LaTex expression showing 43-th root of 6my
b A LaTex expression showing 3-th root of 7my
c A LaTex expression showing 1 over 3-th root of 4{m to the power of 3{y to the power of 3 }}
d A LaTex expression showing 3-th root of 8my
e A LaTex expression showing 33-th root of 4{m to the power of 2 {y} to the power of 3 }