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Radicals - Convert Cube Root, Values and Variables, to Exponents - Positive (Level 2)

This math topic focuses on converting cube roots of numerical values and variables into fractional exponents. The problems involve various algebraic expressions under the cube root symbol, teaching how to express these expressions with positive fractional exponents. This skill is part of the broader advanced simplifying radicals unit. Each problem presents multiple choices to identify the correct conversion into fractional exponents, enhancing understanding of exponent rules and their application in 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, to Exponents - Positive

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Convert the radical to a fractional exponent

5xp43\sqrt[3]{5x{p}^{4}}

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 2)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 7d{p to the power of 4 }
a A LaTex expression showing 7 to the power of 1 over 2 times d to the power of 1 over 2 times {p} to the power of 4 over 2
b A LaTex expression showing 21 to the power of 1 over 3 times d to the power of 1 over 3 times {p} to the power of 4 over 3
c A LaTex expression showing 7 to the power of 1 over 3 times d to the power of 1 over 3 times {p} to the power of 4 over 3
d A LaTex expression showing 7 to the power of 1 over 3 times {d} to the power of 3 over 3 times {p} to the power of 6 over 3
e A LaTex expression showing 7 to the power of -1 over 3 times d to the power of -1 over 3 times {p} to the power of -4 over 3
f A LaTex expression showing 28 to the power of 1 over 3 times d to the power of 1 over 3 times {p} to the power of 4 over 3
2
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 2{z to the power of 4 {r} to the power of 4 }
a A LaTex expression showing 8 to the power of 1 over 3 times {z} to the power of 4 over 3 times {r} to the power of 4 over 3
b A LaTex expression showing 2 to the power of -1 over 3 times {z} to the power of -4 over 3 times {r} to the power of -4 over 3
c A LaTex expression showing 6 to the power of 1 over 3 times {z} to the power of 4 over 3 times {r} to the power of 4 over 3
d A LaTex expression showing 2 to the power of 1 over 3 times {z} to the power of 4 over 3 times {r} to the power of 4 over 3
e A LaTex expression showing 2 to the power of 1 over 3 times {z} to the power of 4 over 3 times {r} to the power of 5 over 3
f A LaTex expression showing 2 to the power of 1 over 2 times {z} to the power of 4 over 2 times {r} to the power of 4 over 2
3
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 2{d to the power of 5 {b} to the power of 4 }
a A LaTex expression showing 6 to the power of 1 over 3 times {d} to the power of 5 over 3 times {b} to the power of 4 over 3
b A LaTex expression showing 2 to the power of 1 over 3 times {d} to the power of 4 over 3 times {b} to the power of 3 over 3
c A LaTex expression showing 2 to the power of 1 over 3 times {d} to the power of 5 over 3 times {b} to the power of 4 over 3
d A LaTex expression showing 2 to the power of 1 over 3 times {d} to the power of 5 over 3 times {b} to the power of 3 over 3
e A LaTex expression showing 2 to the power of 1 over 3 times {d} to the power of 6 over 3 times {b} to the power of 3 over 3
f A LaTex expression showing 2 to the power of 1 over 2 times {d} to the power of 5 over 2 times {b} to the power of 4 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 7{b to the power of 4 {d} to the power of 2 }
a A LaTex expression showing 21 to the power of 1 over 3 times {b} to the power of 4 over 3 times {d} to the power of 2 over 3
b A LaTex expression showing 7 to the power of 1 over 2 times {b} to the power of 4 over 2 times {d} to the power of 2 over 2
c A LaTex expression showing 7 to the power of 1 over 3 times {b} to the power of 4 over 3 times {d} to the power of 3 over 3
d A LaTex expression showing 14 to the power of 1 over 3 times {b} to the power of 4 over 3 times {d} to the power of 2 over 3
e A LaTex expression showing 7 to the power of -1 over 3 times {b} to the power of -4 over 3 times {d} to the power of -2 over 3
f A LaTex expression showing 7 to the power of 1 over 3 times {b} to the power of 4 over 3 times {d} to the power of 2 over 3
5
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 5{y to the power of 4 z}
a A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 4 over 3 times {z} to the power of 2 over 3
b A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 4 over 3 times z to the power of 1 over 3
c A LaTex expression showing 15 to the power of 1 over 3 times {y} to the power of 4 over 3 times z 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 4 over 3 times {z} to the power of 3 over 3
e A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 6 over 3 times {z} to the power of 2 over 3
f A LaTex expression showing 5 to the power of 1 over 2 times {y} to the power of 4 over 2 times z to the power of 1 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 7{p to the power of 4 {d} to the power of 4 }
a A LaTex expression showing 7 to the power of 1 over 3 times {p} to the power of 6 over 3 times {d} to the power of 4 over 3
b A LaTex expression showing 7 to the power of 1 over 2 times {p} to the power of 4 over 2 times {d} to the power of 4 over 2
c A LaTex expression showing 7 to the power of 1 over 3 times {p} to the power of 3 over 3 times {d} to the power of 4 over 3
d A LaTex expression showing 7 to the power of 1 over 3 times {p} to the power of 3 over 3 times {d} to the power of 3 over 3
e A LaTex expression showing 28 to the power of 1 over 3 times {p} to the power of 4 over 3 times {d} to the power of 4 over 3
f A LaTex expression showing 7 to the power of 1 over 3 times {p} to the power of 4 over 3 times {d} to the power of 4 over 3
7
Convert the radical to a fractional exponent
A LaTex expression showing 3-th root of 3{p to the power of 2 {z} to the power of 4 }
a A LaTex expression showing 3 to the power of 1 over 3 times p to the power of 1 over 3 times {z} to the power of 5 over 3
b A LaTex expression showing 3 to the power of 1 over 3 times {p} to the power of 3 over 3 times {z} to the power of 5 over 3
c A LaTex expression showing 3 to the power of -1 over 3 times {p} to the power of -2 over 3 times {z} to the power of -4 over 3
d A LaTex expression showing 12 to the power of 1 over 3 times {p} to the power of 2 over 3 times {z} to the power of 4 over 3
e A LaTex expression showing 3 to the power of 1 over 3 times {p} to the power of 2 over 3 times {z} to the power of 4 over 3
f A LaTex expression showing 3 to the power of 1 over 2 times {p} to the power of 2 over 2 times {z} to the power of 4 over 2