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

This math topic focuses on converting cube roots involving numbers and variables into expressions with negative fractional exponents. It covers understanding and manipulating the cube root of numeric values and algebraic terms to their equivalent expressions using exponent rules, particularly negative fractional exponents. Each problem presents a radical expression and multiple-choice answers showing different potential conversions to an exponent form, requiring the application of simplifying advanced radicals for accurate conversion.

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

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

Convert the radical to a fractional exponent

13md53\frac{1}{\sqrt[3]{3m{d}^{5}}}

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 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 1 over 3-th root of 11{n to the power of 5{x to the power of 4 }}
a A LaTex expression showing 11 to the power of -1 over 3 times {n} to the power of -5 over 3 times {x} to the power of -5 over 3
b A LaTex expression showing 22 to the power of -1 over 3 times {n} to the power of -5 over 3 times {x} to the power of -4 over 3
c A LaTex expression showing 44 to the power of -1 over 3 times {n} to the power of -5 over 3 times {x} to the power of -4 over 3
d A LaTex expression showing 33 to the power of -1 over 3 times {n} to the power of -5 over 3 times {x} to the power of -4 over 3
e A LaTex expression showing 11 to the power of -1 over 2 times {n} to the power of -5 over 2 times {x} to the power of -4 over 2
f A LaTex expression showing 11 to the power of -1 over 3 times {n} to the power of -5 over 3 times {x} 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 5{p to the power of 4{r to the power of 4 }}
a A LaTex expression showing 10 to the power of -1 over 3 times {p} to the power of -4 over 3 times {r} to the power of -4 over 3
b A LaTex expression showing 5 to the power of -1 over 3 times {p} to the power of -3 over 3 times {r} to the power of -5 over 3
c A LaTex expression showing 5 to the power of -1 over 3 times {p} to the power of -4 over 3 times {r} to the power of -3 over 3
d A LaTex expression showing 5 to the power of -1 over 2 times {p} to the power of -4 over 2 times {r} to the power of -4 over 2
e A LaTex expression showing 5 to the power of -1 over 3 times {p} to the power of -3 over 3 times {r} to the power of -6 over 3
f A LaTex expression showing 5 to the power of -1 over 3 times {p} to the power of -4 over 3 times {r} 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 3{x to the power of 4{d to the power of 2 }}
a A LaTex expression showing 3 to the power of -1 over 3 times {x} to the power of -3 over 3 times {d} to the power of -2 over 3
b A LaTex expression showing 9 to the power of -1 over 3 times {x} to the power of -4 over 3 times {d} to the power of -2 over 3
c A LaTex expression showing 3 to the power of 1 over 3 times {x} to the power of 4 over 3 times {d} to the power of 2 over 3
d A LaTex expression showing 6 to the power of -1 over 3 times {x} to the power of -4 over 3 times {d} to the power of -2 over 3
e A LaTex expression showing 3 to the power of -1 over 3 times {x} to the power of -4 over 3 times {d} to the power of -2 over 3
f A LaTex expression showing 3 to the power of -1 over 2 times {x} to the power of -4 over 2 times {d} to the power of -2 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 2{c to the power of 4{d to the power of 5 }}
a A LaTex expression showing 2 to the power of -1 over 3 times {c} to the power of -6 over 3 times {d} to the power of -7 over 3
b A LaTex expression showing 4 to the power of -1 over 3 times {c} to the power of -4 over 3 times {d} to the power of -5 over 3
c A LaTex expression showing 2 to the power of -1 over 3 times {c} to the power of -3 over 3 times {d} to the power of -4 over 3
d A LaTex expression showing 2 to the power of -1 over 3 times {c} to the power of -4 over 3 times {d} to the power of -5 over 3
e A LaTex expression showing 2 to the power of -1 over 2 times {c} to the power of -4 over 2 times {d} to the power of -5 over 2
f A LaTex expression showing 6 to the power of -1 over 3 times {c} to the power of -4 over 3 times {d} to the power of -5 over 3
5
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 7{n to the power of 4{p to the power of 2 }}
a A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -6 over 3 times {p} to the power of -2 over 3
b A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -4 over 3 times {p} to the power of -3 over 3
c A LaTex expression showing 7 to the power of 1 over 3 times {n} to the power of 4 over 3 times {p} to the power of 2 over 3
d A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -3 over 3 times p to the power of -1 over 3
e A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -4 over 3 times {p} to the power of -2 over 3
f A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -3 over 3 times {p} to the power of -4 over 3
6
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 3{x to the power of 5{b to the power of 4 }}
a A LaTex expression showing 3 to the power of -1 over 2 times {x} to the power of -5 over 2 times {b} to the power of -4 over 2
b A LaTex expression showing 6 to the power of -1 over 3 times {x} to the power of -5 over 3 times {b} to the power of -4 over 3
c A LaTex expression showing 3 to the power of -1 over 3 times {x} to the power of -5 over 3 times {b} to the power of -6 over 3
d A LaTex expression showing 3 to the power of -1 over 3 times {x} to the power of -5 over 3 times {b} to the power of -3 over 3
e A LaTex expression showing 3 to the power of -1 over 3 times {x} to the power of -5 over 3 times {b} to the power of -4 over 3
f A LaTex expression showing 9 to the power of -1 over 3 times {x} to the power of -5 over 3 times {b} to the power of -4 over 3
7
Convert the radical to a fractional exponent
A LaTex expression showing 1 over 3-th root of 7n{d to the power of 4 }
a A LaTex expression showing 7 to the power of -1 over 2 times n to the power of -1 over 2 times {d} to the power of -4 over 2
b A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -2 over 3 times {d} to the power of -3 over 3
c A LaTex expression showing 7 to the power of -1 over 3 times n to the power of -1 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 {n} to the power of -3 over 3 times {d} to the power of -6 over 3
e A LaTex expression showing 7 to the power of -1 over 3 times n to the power of -1 over 3 times {d} to the power of -6 over 3
f A LaTex expression showing 7 to the power of -1 over 3 times {n} to the power of -3 over 3 times {d} to the power of -4 over 3