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

This math topic focuses on converting fractional exponents to radical form, specifically those with negative exponents. The problems involve various constants and variables raised to negative fractional powers, and students are tasked with expressing these in cube root form. Each question presents an expression with fractional powers of different bases, including variables and constants, which students must convert to radicals. The exercises are advanced and fall under the unit of simplifying radicals, helping students deepen their understanding of exponents and roots.

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 - Negative

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

Convert the fractional exponent to a radical

11−13⋅c−43⋅d−2311^{-\frac{1}{3}}\cdot {c}^{-\frac{4}{3}}\cdot {d}^{-\frac{2}{3}}

Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative Worksheet

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Math worksheet on 'Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative (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 {y} to the power of -4 over 3 times m to the power of -1 over 3
a A LaTex expression showing 1 over y3-th root of {y to the power of 2{m to the power of 3 }}
b A LaTex expression showing 1 over y3-th root of 6{y to the power of 2m }
c A LaTex expression showing 1 over 3{y to the power of 3 3-th root of 2{y to the power of 3 m}}
d A LaTex expression showing 1 over 3{y to the power of 2 3-th root of 6{y to the power of 3 m}}
e A LaTex expression showing 1 over y3-th root of ym
f A LaTex expression showing 1 over 3-th root of 3{y to the power of 4m }
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 3 times {r} to the power of -4 over 3 times {d} to the power of -5 over 3
a A LaTex expression showing 1 over 4{r to the power of 2 {d} to the power of 3 3-th root of 7{r to the power of 3 d}}
b A LaTex expression showing 1 over {r to the power of 3 {d} to the power of 2 3-th root of 7r{d to the power of 2 }}
c A LaTex expression showing 1 over r{d to the power of 3 3-th root of 3r{d to the power of 3 }}
d A LaTex expression showing 1 over 3-th root of 7{r to the power of 4{d to the power of 5 }}
e A LaTex expression showing 1 over 2{r to the power of 3 {d} to the power of 3 3-th root of 4{r to the power of 2 {d} to the power of 4 }}
f A LaTex expression showing 1 over 4rd3-th root of 4rd
3
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 -4 over 3 times {b} to the power of -2 over 3
a A LaTex expression showing 1 over x3-th root of 3{x to the power of 2b }
b A LaTex expression showing 1 over 3-th root of 7{x to the power of 4{b to the power of 2 }}
c A LaTex expression showing 1 over x3-th root of 4x{b to the power of 2 }
d A LaTex expression showing 1 over {x to the power of 2 3-th root of 9x{b to the power of 3 }}
e A LaTex expression showing 1 over {x to the power of 2 3-th root of 4{x to the power of 2 b}}
f A LaTex expression showing 1 over x3-th root of 10{x to the power of 3b }
4
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 -5 over 3 times {d} to the power of -2 over 3
a A LaTex expression showing 1 over {m to the power of 3 3-th root of 8{m to the power of 2 {d} to the power of 4 }}
b A LaTex expression showing 1 over {m to the power of 2 3-th root of 7m{d to the power of 4 }}
c A LaTex expression showing 1 over 3-th root of 11{m to the power of 5{d to the power of 2 }}
d A LaTex expression showing 1 over 4{m to the power of 3 3-th root of 8{m to the power of 4 {d} to the power of 2 }}
e A LaTex expression showing 1 over 4{m to the power of 2 3-th root of 11{m to the power of 2 {d} to the power of 2 }}
f A LaTex expression showing 1 over {m to the power of 3 3-th root of 7{m to the power of 2 {d} to the power of 3 }}
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 -1 over 3 times {p} to the power of -2 over 3
a A LaTex expression showing 1 over 3-th root of 3m{p to the power of 2 }
b A LaTex expression showing 1 over 3-th root of mp
c A LaTex expression showing 1 over 3-th root of m{p to the power of 3 }
d A LaTex expression showing 1 over 3-th root of {m to the power of 3{p to the power of 2 }}
e A LaTex expression showing 1 over 3-th root of 4m{p to the power of 4 }
f A LaTex expression showing 1 over 23-th root of 6m{p to the power of 3 }
6
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 {y} to the power of -2 over 3
a A LaTex expression showing 1 over 3m3-th root of 10m{y to the power of 4 }
b A LaTex expression showing 1 over {m to the power of 2 3-th root of 6m{y to the power of 3 }}
c A LaTex expression showing 1 over 3-th root of 7{m to the power of 4{y to the power of 2 }}
d A LaTex expression showing 1 over {m to the power of 2 3-th root of 4{m to the power of 2 {y} to the power of 3 }}
e A LaTex expression showing 1 over m3-th root of 10{m to the power of 3y }
f A LaTex expression showing 1 over {m to the power of 2 3-th root of 7my}
7
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 -4 over 3 times {c} to the power of -4 over 3
a A LaTex expression showing 1 over 3{b to the power of 3 c3-th root of b{c to the power of 3 }}
b A LaTex expression showing 1 over 3{b to the power of 3 {c} to the power of 3 3-th root of bc}
c A LaTex expression showing 1 over bc3-th root of 4{b to the power of 2{c to the power of 3 }}
d A LaTex expression showing 1 over 3-th root of 3{b to the power of 4{c to the power of 4 }}
e A LaTex expression showing 1 over {b to the power of 2 {c} to the power of 3 3-th root of bc}
f A LaTex expression showing 1 over bc3-th root of 6bc