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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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 z to the power of -1 over 3 times {n} to the power of -4 over 3
a A LaTex expression showing 1 over n3-th root of 4z{n to the power of 3 }
b A LaTex expression showing n3-th root of z{n to the power of 2 }
c A LaTex expression showing 1 over 3-th root of 3z{n to the power of 4 }
d A LaTex expression showing 1 over 4n3-th root of zn
e A LaTex expression showing 1 over 4n3-th root of 4zn
2
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 {y} to the power of -2 over 3
a A LaTex expression showing x3-th root of 7{x to the power of 2 y}
b A LaTex expression showing 1 over {x to the power of 3 3-th root of 14x{y to the power of 4 }}
c A LaTex expression showing 1 over 4x3-th root of 13x{y to the power of 4 }
d A LaTex expression showing 1 over x3-th root of 11x{y to the power of 3 }
e A LaTex expression showing 1 over 3-th root of 11{x to the power of 4{y 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 {n} to the power of -2 over 3 times {b} to the power of -4 over 3
a A LaTex expression showing {b} to the power of 3 3-th root of 5nb
b A LaTex expression showing 1 over 3b3-th root of 6nb
c A LaTex expression showing 1 over b3-th root of 6{n to the power of 4b }
d A LaTex expression showing 1 over b3-th root of 2nb
e A LaTex expression showing 1 over 3-th root of 5{n to the power of 2{b to the power of 4 }}
4
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 -1 over 3 times {r} to the power of -5 over 3
a A LaTex expression showing 1 over 2{r to the power of 3 3-th root of 8{c to the power of 2 {r} to the power of 4 }}
b A LaTex expression showing 1 over 3-th root of 11c{r to the power of 5 }
c A LaTex expression showing 1 over {r to the power of 2 3-th root of 14{c to the power of 3 {r} to the power of 3 }}
d A LaTex expression showing 1 over r3-th root of 12cr
e A LaTex expression showing 2r3-th root of 14c{r 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 {y} to the power of -5 over 3 times {d} to the power of -5 over 3
a A LaTex expression showing 1 over 3-th root of 3{y to the power of 5{d to the power of 5 }}
b A LaTex expression showing 1 over y{d to the power of 3 3-th root of 3{y to the power of 4 d}}
c A LaTex expression showing y{d} to the power of 2 3-th root of yd
d A LaTex expression showing 1 over 4{y to the power of 2 d3-th root of 3{y to the power of 3 {d} to the power of 3 }}
e A LaTex expression showing 1 over {y to the power of 2 d3-th root of yd}
6
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 -1 over 3 times {n} to the power of -4 over 3
a A LaTex expression showing 1 over 3n3-th root of 9{x to the power of 2n }
b A LaTex expression showing 1 over 3-th root of 7x{n to the power of 4 }
c A LaTex expression showing {n} to the power of 2 3-th root of 6{x to the power of 3 n}
d A LaTex expression showing 1 over 2{n to the power of 2 3-th root of 9xn}
e A LaTex expression showing 1 over {n to the power of 2 3-th root of 5{x to the power of 3 n}}
7
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times {b} to the power of -5 over 3 times n to the power of -1 over 3
a A LaTex expression showing b3-th root of {b to the power of 4 {n} to the power of 2 }
b A LaTex expression showing 1 over b3-th root of 3bn
c A LaTex expression showing 1 over 3-th root of 2{b to the power of 5n }
d A LaTex expression showing 1 over {b to the power of 2 3-th root of {b to the power of 2 n}}
e A LaTex expression showing 1 over b3-th root of 2{b to the power of 3n }