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

This math topic focuses on simplifying radicals and converting cube roots, involving both numerical values and variables, into negative fractional exponents. The exercises test the ability to express cube roots in exponent form, fostering an understanding of how to work with powers and roots effectively. Each question provides multiple choice answers where students practice converting expressions such as cube roots of products of numbers and variables into their corresponding exponential forms with negative exponents. This topic falls under a broader unit of simplifying radicals, enhancing the student's algebraic manipulation skills.

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, to Exponents - Negative

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Convert the radical to a fractional exponent

111m23\frac{1}{\sqrt[3]{11{m}^{2}}}

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

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Math worksheet on 'Radicals - Convert Cube Root, Values and Variables, to 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 radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 11{d to the power of 4 }
a A LaTex expression showing 11 to the power of -1 over 3 times {d} to the power of -6 over 3
b A LaTex expression showing 33 to the power of -1 over 3 times {d} to the power of -4 over 3
c A LaTex expression showing 11 to the power of 1 over 3 times {d} to the power of 4 over 3
d A LaTex expression showing 44 to the power of -1 over 3 times {d} to the power of -4 over 3
e A LaTex expression showing 11 to the power of -1 over 2 times {d} to the power of -4 over 2
f A LaTex expression showing 11 to the power of -1 over 3 times {d} to the power of -4 over 3
2
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 2{y to the power of 2 }
a A LaTex expression showing 2 to the power of -1 over 3 times {y} to the power of -2 over 3
b A LaTex expression showing 6 to the power of -1 over 3 times {y} to the power of -2 over 3
c A LaTex expression showing 2 to the power of 1 over 3 times {y} to the power of 2 over 3
d A LaTex expression showing 4 to the power of -1 over 3 times {y} to the power of -2 over 3
e A LaTex expression showing 2 to the power of -1 over 2 times {y} to the power of -2 over 2
f A LaTex expression showing 8 to the power of -1 over 3 times {y} to the power of -2 over 3
3
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 11{x to the power of 4 }
a A LaTex expression showing 33 to the power of -1 over 3 times {x} to the power of -4 over 3
b A LaTex expression showing 11 to the power of -1 over 3 times {x} to the power of -3 over 3
c A LaTex expression showing 11 to the power of -1 over 3 times {x} to the power of -4 over 3
d A LaTex expression showing 11 to the power of -1 over 2 times {x} to the power of -4 over 2
e A LaTex expression showing 44 to the power of -1 over 3 times {x} to the power of -4 over 3
f A LaTex expression showing 22 to the power of -1 over 3 times {x} to the power of -4 over 3
4
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 3p
a A LaTex expression showing 9 to the power of -1 over 3 times p to the power of -1 over 3
b A LaTex expression showing 3 to the power of 1 over 3 times p to the power of 1 over 3
c A LaTex expression showing 3 to the power of -1 over 3 times {p} to the power of -2 over 3
d A LaTex expression showing 3 to the power of -1 over 3 times p to the power of -1 over 3
e A LaTex expression showing 3 to the power of -1 over 3
f A LaTex expression showing 12 to the power of -1 over 3 times p to the power of -1 over 3
5
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 11{r to the power of 4 }
a A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -6 over 3
b A LaTex expression showing 11 to the power of 1 over 3 times {r} to the power of 4 over 3
c A LaTex expression showing 33 to the power of -1 over 3 times {r} to the power of -4 over 3
d A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -5 over 3
e A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -4 over 3
f A LaTex expression showing 11 to the power of -1 over 3 times {r} to the power of -3 over 3
6
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 3d
a A LaTex expression showing 3 to the power of -1 over 3 times d to the power of -1 over 3
b A LaTex expression showing 12 to the power of -1 over 3 times d to the power of -1 over 3
c A LaTex expression showing 3 to the power of -1 over 2 times d to the power of -1 over 2
d A LaTex expression showing 3 to the power of -1 over 3 times {d} to the power of -3 over 3
e A LaTex expression showing 6 to the power of -1 over 3 times d to the power of -1 over 3
f A LaTex expression showing 3 to the power of 1 over 3 times d to the power of 1 over 3
7
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 11{m to the power of 2 }
a A LaTex expression showing 33 to the power of -1 over 3 times {m} to the power of -2 over 3
b A LaTex expression showing 11 to the power of -1 over 3 times {m} to the power of -3 over 3
c A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -2 over 2
d A LaTex expression showing 11 to the power of -1 over 3 times {m} to the power of -2 over 3
e A LaTex expression showing 44 to the power of -1 over 3 times {m} to the power of -2 over 3
f A LaTex expression showing 11 to the power of -1 over 3 times {m} to the power of -4 over 3