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

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Radicals - Convert Cube Root, Values and Variables, to Exponents - Negative
1
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 3{r to the power of 2 }
a A LaTex expression showing 3 to the power of -1 over 3 times {r} to the power of -3 over 3
b A LaTex expression showing 3 to the power of -1 over 3 times r to the power of -1 over 3
c A LaTex expression showing 3 to the power of 1 over 3 times {r} to the power of 2 over 3
d A LaTex expression showing 3 to the power of -1 over 3 times {r} to the power of -2 over 3
2
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 5{m to the power of 4 }
a A LaTex expression showing 20 to the power of -1 over 3 times {m} to the power of -4 over 3
b A LaTex expression showing 10 to the power of -1 over 3 times {m} to the power of -4 over 3
c A LaTex expression showing 5 to the power of -1 over 3 times {m} to the power of -4 over 3
d A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -4 over 2
e A LaTex expression showing 5 to the power of 1 over 3 times {m} to the power of 4 over 3
3
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 5x
a A LaTex expression showing 5 to the power of -1 over 3 times {x} to the power of -3 over 3
b A LaTex expression showing 5 to the power of 1 over 3 times x to the power of 1 over 3
c A LaTex expression showing 5 to the power of -1 over 3 times x to the power of -1 over 3
d A LaTex expression showing 20 to the power of -1 over 3 times x to the power of -1 over 3
4
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 5c
a A LaTex expression showing 10 to the power of -1 over 3 times c to the power of -1 over 3
b A LaTex expression showing 5 to the power of -1 over 3 times c to the power of -1 over 3
c A LaTex expression showing 5 to the power of -1 over 3 times {c} to the power of -2 over 3
d A LaTex expression showing 15 to the power of -1 over 3 times c to the power of -1 over 3
e A LaTex expression showing 5 to the power of -1 over 3 times {c} to the power of -3 over 3
5
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 11d
a A LaTex expression showing 11 to the power of -1 over 3 times {d} to the power of -3 over 3
b A LaTex expression showing 33 to the power of -1 over 3 times d to the power of -1 over 3
c A LaTex expression showing 11 to the power of -1 over 3 times d to the power of -1 over 3
d A LaTex expression showing 11 to the power of 1 over 3 times d to the power of 1 over 3
e A LaTex expression showing 11 to the power of -1 over 2 times d to the power of -1 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 2x
a A LaTex expression showing 4 to the power of -1 over 3 times x to the power of -1 over 3
b A LaTex expression showing 8 to the power of -1 over 3 times x to the power of -1 over 3
c A LaTex expression showing 2 to the power of 1 over 3 times x to the power of 1 over 3
d A LaTex expression showing 2 to the power of -1 over 3 times {x} to the power of -2 over 3
e A LaTex expression showing 2 to the power of -1 over 3 times x 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 2{n to the power of 4 }
a A LaTex expression showing 6 to the power of -1 over 3 times {n} to the power of -4 over 3
b A LaTex expression showing 2 to the power of 1 over 3 times {n} to the power of 4 over 3
c A LaTex expression showing 2 to the power of -1 over 3 times {n} to the power of -4 over 3
d A LaTex expression showing 4 to the power of -1 over 3 times {n} to the power of -4 over 3
8
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 3{n to the power of 2 }
a A LaTex expression showing 3 to the power of -1 over 2 times {n} to the power of -2 over 2
b A LaTex expression showing 3 to the power of -1 over 3 times n to the power of -1 over 3
c A LaTex expression showing 3 to the power of -1 over 3 times {n} to the power of -2 over 3
d A LaTex expression showing 9 to the power of -1 over 3 times {n} to the power of -2 over 3
e A LaTex expression showing 6 to the power of -1 over 3 times {n} to the power of -2 over 3