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Radicals - Convert Cube Root, Values and Variables, from Exponents - Negative (Level 1)

This math topic focuses on converting fractional exponents to radical forms, specifically dealing with negative exponents and cube roots. It practices simplifying complex expressions involving powers and roots of numerical values and variables. The problems involve interpreting expressions with negative fractional exponents and expressing them as radicals, aiding in developing skills in simplification and manipulation of exponent and radical expressions.

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

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Convert the fractional exponent to a radical

3−13⋅b−233^{-\frac{1}{3}}\cdot {b}^{-\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 1)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
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 -2 over 3
a A LaTex expression showing 1 over 3-th root of b
b A LaTex expression showing 1 over 3-th root of {b to the power of 2 }
c A LaTex expression showing 1 over 33-th root of 4{b to the power of 2 }
d A LaTex expression showing 1 over 33-th root of 3{b to the power of 2 }
e A LaTex expression showing 1 over 43-th root of 4b
f A LaTex expression showing 1 over 3-th root of 3{b to the power of 2 }
2
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times x to the power of -1 over 3
a A LaTex expression showing 1 over 3-th root of 2x
b A LaTex expression showing 1 over 3-th root of x
c A LaTex expression showing 1 over 23-th root of x
d A LaTex expression showing 1 over 43-th root of 4{x to the power of 2 }
e A LaTex expression showing 1 over 23-th root of 3{x to the power of 2 }
f A LaTex expression showing 1 over 33-th root of 5{x to the power of 3 }
3
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 -2 over 3
a A LaTex expression showing 1 over 43-th root of {d to the power of 4 }
b A LaTex expression showing 1 over 3-th root of 7{d to the power of 3 }
c A LaTex expression showing 1 over 3-th root of 5{d to the power of 2 }
d A LaTex expression showing 1 over 3-th root of 3{d to the power of 2 }
e A LaTex expression showing 1 over 33-th root of 5{d to the power of 2 }
f A LaTex expression showing 1 over 23-th root of 8d
4
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 -1 over 3
a A LaTex expression showing 1 over 3-th root of 2b
b A LaTex expression showing 1 over 23-th root of b
c A LaTex expression showing 1 over 3-th root of 5b
d A LaTex expression showing 1 over 23-th root of 2b
e A LaTex expression showing 1 over 3-th root of b
f A LaTex expression showing 1 over 3-th root of 4b
5
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 3 times {n} to the power of -2 over 3
a A LaTex expression showing 1 over 3-th root of 12n
b A LaTex expression showing 1 over 23-th root of 13{n to the power of 4 }
c A LaTex expression showing 1 over 33-th root of 10n
d A LaTex expression showing 1 over 3-th root of 8n
e A LaTex expression showing 1 over 3-th root of 11{n to the power of 2 }
f A LaTex expression showing 1 over 3-th root of 11n
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 3 times r to the power of -1 over 3
a A LaTex expression showing 1 over 23-th root of 2r
b A LaTex expression showing 1 over 3-th root of 3{r to the power of 3 }
c A LaTex expression showing 1 over 3-th root of 2{r to the power of 3 }
d A LaTex expression showing 1 over 3-th root of {r to the power of 3 }
e A LaTex expression showing 1 over 3-th root of 5r
f A LaTex expression showing 1 over 3-th root of 2r
7
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 3 times z to the power of -1 over 3
a A LaTex expression showing 1 over 3-th root of 11z
b A LaTex expression showing 1 over 43-th root of 9z
c A LaTex expression showing 1 over 3-th root of 7{z to the power of 2 }
d A LaTex expression showing 1 over 33-th root of 14z
e A LaTex expression showing 1 over 23-th root of 13z
f A LaTex expression showing 1 over 3-th root of 8z