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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Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative
1
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 r to the power of -1 over 3
a A LaTex expression showing 1 over 3-th root of 7xr
b A LaTex expression showing 1 over 23-th root of 5{x to the power of 2{r to the power of 3 }}
c A LaTex expression showing 1 over 33-th root of 8xr
d A LaTex expression showing 1 over 3-th root of 6xr
e A LaTex expression showing 43-th root of 5x{r to the power of 2 }
2
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 -4 over 3 times b to the power of -1 over 3
a A LaTex expression showing z3-th root of zb
b A LaTex expression showing 1 over 3-th root of 3{z to the power of 4b }
c A LaTex expression showing 1 over 2z3-th root of 6zb
d A LaTex expression showing 1 over {z to the power of 3 3-th root of 3z{b to the power of 2 }}
e A LaTex expression showing 1 over {z to the power of 3 3-th root of 4zb}
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 -1 over 3 times {n} to the power of -4 over 3
a A LaTex expression showing 1 over 2{n to the power of 2 3-th root of 9xn}
b A LaTex expression showing 1 over 3n3-th root of 9{x to the power of 2n }
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 {n to the power of 2 3-th root of 5{x to the power of 3 n}}
e A LaTex expression showing 1 over 3-th root of 7x{n to the power of 4 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 3 times {x} to the power of -4 over 3 times {r} to the power of -4 over 3
a A LaTex expression showing xr3-th root of 6xr
b A LaTex expression showing 1 over 3-th root of 5{x to the power of 4{r to the power of 4 }}
c A LaTex expression showing 1 over 2xr3-th root of 2{x to the power of 2{r to the power of 2 }}
d A LaTex expression showing 1 over x{r to the power of 2 3-th root of 6x{r to the power of 3 }}
e A LaTex expression showing 1 over x{r to the power of 3 3-th root of 3{x to the power of 2 {r} to the power of 2 }}
5
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times {c} to the power of -5 over 3 times x to the power of -1 over 3
a A LaTex expression showing c3-th root of 2{c to the power of 3 x}
b A LaTex expression showing 1 over 2c3-th root of 2{c to the power of 4x }
c A LaTex expression showing 1 over {c to the power of 2 3-th root of 2cx}
d A LaTex expression showing 1 over c3-th root of {c to the power of 3{x to the power of 2 }}
e A LaTex expression showing 1 over 3-th root of 2{c to the power of 5x }
6
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -4 over 3 times m to the power of -1 over 3
a A LaTex expression showing 1 over 3r3-th root of 8rm
b A LaTex expression showing 1 over 3-th root of 11{r to the power of 4m }
c A LaTex expression showing 1 over r3-th root of 8{r to the power of 2m }
d A LaTex expression showing r3-th root of 12{r to the power of 2 {m} to the power of 3 }
e A LaTex expression showing 1 over r3-th root of 9rm
7
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 -5 over 3 times {n} to the power of -5 over 3
a A LaTex expression showing d{n} to the power of 3 3-th root of 4{d to the power of 3 {n} to the power of 4 }
b A LaTex expression showing 1 over {d to the power of 3 n3-th root of 4{d to the power of 4 n}}
c A LaTex expression showing 1 over {d to the power of 2 n3-th root of 7{d to the power of 3 n}}
d A LaTex expression showing 1 over 3-th root of 5{d to the power of 5{n to the power of 5 }}
e A LaTex expression showing 1 over 2dn3-th root of 2d{n to the power of 3 }
8
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 -2 over 3 times {z} to the power of -5 over 3
a A LaTex expression showing 1 over {z to the power of 3 3-th root of 6x{z to the power of 4 }}
b A LaTex expression showing 1 over 3-th root of 3{x to the power of 2{z to the power of 5 }}
c A LaTex expression showing 2z3-th root of 4xz
d A LaTex expression showing 1 over z3-th root of 2x{z to the power of 2 }
e A LaTex expression showing 1 over 3{z to the power of 2 3-th root of 3xz}