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

This math topic revolves around converting cube roots to fractional exponents, focusing on numerical and variable expressions. It forms part of a broader unit on simplifying radicals. Each question presents a radical and asks to transform it into an expression with exponents in fractional form, providing multiple choices. This skill is foundational for understanding higher-level algebraic operations and streamlining calculation processes involving roots and powers.

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 - Positive

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Convert the radical to a fractional exponent

5y3\sqrt[3]{5y}

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

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Math worksheet on 'Radicals - Convert Cube Root, Values and Variables, to Exponents - Positive (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 3-th root of 11y
a A LaTex expression showing 11 to the power of -1 over 3 times y to the power of -1 over 3
b A LaTex expression showing 11 to the power of 1 over 3
c A LaTex expression showing 11 to the power of 1 over 3 times {y} to the power of 3 over 3
d A LaTex expression showing 11 to the power of 1 over 3 times y to the power of 1 over 3
e A LaTex expression showing 11 to the power of 1 over 2 times y to the power of 1 over 2
f A LaTex expression showing 22 to the power of 1 over 3 times y to the power of 1 over 3
2
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 5{m to the power of 2 }
a A LaTex expression showing 10 to the power of 1 over 3 times {m} to the power of 2 over 3
b A LaTex expression showing 5 to the power of -1 over 3 times {m} to the power of -2 over 3
c A LaTex expression showing 15 to the power of 1 over 3 times {m} to the power of 2 over 3
d A LaTex expression showing 5 to the power of 1 over 3 times {m} to the power of 4 over 3
e A LaTex expression showing 5 to the power of 1 over 3 times {m} to the power of 2 over 3
f A LaTex expression showing 20 to the power of 1 over 3 times {m} to the power of 2 over 3
3
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 5y
a A LaTex expression showing 5 to the power of 1 over 3 times y to the power of 1 over 3
b A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 2 over 3
c A LaTex expression showing 5 to the power of -1 over 3 times y to the power of -1 over 3
d A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 3 over 3
e A LaTex expression showing 10 to the power of 1 over 3 times y to the power of 1 over 3
f A LaTex expression showing 20 to the power of 1 over 3 times y to the power of 1 over 3
4
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 11{b to the power of 4 }
a A LaTex expression showing 11 to the power of 1 over 3 times {b} to the power of 6 over 3
b A LaTex expression showing 33 to the power of 1 over 3 times {b} to the power of 4 over 3
c A LaTex expression showing 11 to the power of 1 over 2 times {b} to the power of 4 over 2
d A LaTex expression showing 11 to the power of -1 over 3 times {b} to the power of -4 over 3
e A LaTex expression showing 11 to the power of 1 over 3 times {b} to the power of 3 over 3
f A LaTex expression showing 11 to the power of 1 over 3 times {b} to the power of 4 over 3
5
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 7c
a A LaTex expression showing 28 to the power of 1 over 3 times c to the power of 1 over 3
b A LaTex expression showing 14 to the power of 1 over 3 times c to the power of 1 over 3
c A LaTex expression showing 21 to the power of 1 over 3 times c to the power of 1 over 3
d A LaTex expression showing 7 to the power of -1 over 3 times c to the power of -1 over 3
e A LaTex expression showing 7 to the power of 1 over 3 times c to the power of 1 over 3
f A LaTex expression showing 7 to the power of 1 over 3 times {c} to the power of 2 over 3
6
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 7d
a A LaTex expression showing 7 to the power of 1 over 3 times d to the power of 1 over 3
b A LaTex expression showing 14 to the power of 1 over 3 times d to the power of 1 over 3
c A LaTex expression showing 21 to the power of 1 over 3 times d to the power of 1 over 3
d A LaTex expression showing 28 to the power of 1 over 3 times d to the power of 1 over 3
e A LaTex expression showing 7 to the power of 1 over 2 times d to the power of 1 over 2
f A LaTex expression showing 7 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 3-th root of 2r
a A LaTex expression showing 2 to the power of 1 over 3 times {r} to the power of 3 over 3
b A LaTex expression showing 2 to the power of 1 over 3 times r to the power of 1 over 3
c A LaTex expression showing 4 to the power of 1 over 3 times r to the power of 1 over 3
d A LaTex expression showing 2 to the power of 1 over 2 times r to the power of 1 over 2
e A LaTex expression showing 6 to the power of 1 over 3 times r to the power of 1 over 3
f A LaTex expression showing 2 to the power of 1 over 3 times {r} to the power of 2 over 3