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Radicals - Convert Square Root, Values and Variables, from Exponents - Negative (Level 2)

This math topic focuses on converting fractional exponents to radicals, which involves simplifying expressions that contain negative exponents. The problems require knowledge of how to handle powers and roots, particularly in the context of variables and constants. Each problem presents a mathematical expression with variables raised to negative fractional powers, and the student must convert these into radical form, choosing the correct option among multiple answers. This practice is part of a broader unit on simplifying radicals, enhancing problem-solving skills related to algebraic manipulation and exponent rules.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Convert Square Root, Values and Variables, from Exponents - Negative

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

Convert the fractional exponent to a radical

5−12⋅z−32⋅m−325^{-\frac{1}{2}}\cdot {z}^{-\frac{3}{2}}\cdot {m}^{-\frac{3}{2}}

Radicals - Convert Square Root, Values and Variables, from Exponents - Negative Worksheet

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Math worksheet on 'Radicals - Convert Square Root, Values and Variables, from Exponents - Negative (Level 2)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times c to the power of -1 over 2 times {m} to the power of -3 over 2
a A LaTex expression showing 1 over msquare root of {c to the power of 2m }
b A LaTex expression showing 1 over square root of 2c{m to the power of 3 }
c A LaTex expression showing 1 over 3{m to the power of 3 square root of 2cm}
d A LaTex expression showing 1 over msquare root of cm
e A LaTex expression showing 1 over msquare root of c{m to the power of 2 }
f A LaTex expression showing 1 over 2msquare root of 5c{m to the power of 2 }
2
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {z} to the power of -3 over 2 times {m} to the power of -3 over 2
a A LaTex expression showing 1 over 2zmsquare root of 7{z to the power of 3m }
b A LaTex expression showing 1 over z{m to the power of 3 square root of 5zm}
c A LaTex expression showing 1 over zmsquare root of 8zm
d A LaTex expression showing 1 over 4{z to the power of 2 msquare root of 5zm}
e A LaTex expression showing 1 over square root of 5{z to the power of 3{m to the power of 3 }}
f A LaTex expression showing 1 over z{m to the power of 2 square root of 3{z to the power of 2 {m} to the power of 2 }}
3
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times {y} to the power of -5 over 2 times {d} to the power of -3 over 2
a A LaTex expression showing 1 over {y to the power of 2 {d} to the power of 2 square root of 2{y to the power of 3 d}}
b A LaTex expression showing 1 over 2{y to the power of 2 {d} to the power of 3 square root of yd}
c A LaTex expression showing 1 over y{d to the power of 3 square root of 5{y to the power of 2 d}}
d A LaTex expression showing 1 over ydsquare root of 2y{d to the power of 3 }
e A LaTex expression showing 1 over 3ydsquare root of y{d to the power of 3 }
f A LaTex expression showing 1 over square root of 2{y to the power of 5{d to the power of 3 }}
4
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {d} to the power of -3 over 2 times {r} to the power of -5 over 2
a A LaTex expression showing 1 over 3d{r to the power of 3 square root of 6dr}
b A LaTex expression showing 1 over d{r to the power of 4 square root of 2{d to the power of 2 {r} to the power of 3 }}
c A LaTex expression showing 1 over 2drsquare root of 4d{r to the power of 2 }
d A LaTex expression showing 1 over square root of 5{d to the power of 3{r to the power of 5 }}
e A LaTex expression showing 1 over {d to the power of 2 {r} to the power of 2 square root of 6{d to the power of 3 {r} to the power of 2 }}
f A LaTex expression showing 1 over {d to the power of 2 {r} to the power of 2 square root of 5dr}
5
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times c to the power of -1 over 2 times {b} to the power of -3 over 2
a A LaTex expression showing 1 over square root of 5c{b to the power of 3 }
b A LaTex expression showing 1 over bsquare root of 6cb
c A LaTex expression showing 1 over bsquare root of 8c{b to the power of 3 }
d A LaTex expression showing 1 over 4bsquare root of cb
e A LaTex expression showing 1 over bsquare root of 5{c to the power of 3b }
f A LaTex expression showing 1 over 4{b to the power of 3 square root of 5cb}
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times {r} to the power of -3 over 2 times {n} to the power of -5 over 2
a A LaTex expression showing 1 over {r to the power of 3 {n} to the power of 2 square root of {r to the power of 3 {n} to the power of 3 }}
b A LaTex expression showing 1 over 3{r to the power of 2 {n} to the power of 4 square root of {r to the power of 3 n}}
c A LaTex expression showing 1 over square root of 2{r to the power of 3{n to the power of 5 }}
d A LaTex expression showing 1 over rnsquare root of {r to the power of 3n }
e A LaTex expression showing 1 over 3r{n to the power of 3 square root of rn}
f A LaTex expression showing 1 over {r to the power of 2 nsquare root of {r to the power of 2 n}}
7
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {m} to the power of -5 over 2 times {p} to the power of -5 over 2
a A LaTex expression showing 1 over {m to the power of 2 psquare root of 4{m to the power of 2 {p} to the power of 3 }}
b A LaTex expression showing 1 over square root of 5{m to the power of 5{p to the power of 5 }}
c A LaTex expression showing 1 over {m to the power of 2 {p} to the power of 4 square root of 7m{p to the power of 2 }}
d A LaTex expression showing 1 over mpsquare root of 5m{p to the power of 3 }
e A LaTex expression showing 1 over {m to the power of 3 psquare root of 4m{p to the power of 2 }}
f A LaTex expression showing 1 over {m to the power of 2 psquare root of 2{m to the power of 3 p}}