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

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Convert the fractional exponent to a radical

312y52d523^{-\frac{1}{2}}\cdot {y}^{-\frac{5}{2}}\cdot {d}^{-\frac{5}{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 5 to the power of -1 over 2 times {x} to the power of -3 over 2 times {z} to the power of -5 over 2
a A LaTex expression showing 1 over square root of 5{x to the power of 3{z to the power of 5 }}
b A LaTex expression showing 1 over 4x{z to the power of 4 square root of 4xz}
c A LaTex expression showing 1 over x{z to the power of 2 square root of 8{x to the power of 3 z}}
d A LaTex expression showing 1 over {x to the power of 2 zsquare root of 3xz}
e A LaTex expression showing 1 over {x to the power of 2 {z} to the power of 4 square root of 2x{z to the power of 2 }}
f A LaTex expression showing 1 over x{z to the power of 4 square root of {x to the power of 2 z}}
2
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 -1 over 2 times {x} to the power of -3 over 2
a A LaTex expression showing 1 over {x to the power of 3 square root of rx}
b A LaTex expression showing 1 over xsquare root of 4{r to the power of 2{x to the power of 2 }}
c A LaTex expression showing 1 over xsquare root of 3rx
d A LaTex expression showing 1 over 2xsquare root of {r to the power of 3{x to the power of 3 }}
e A LaTex expression showing 1 over square root of 2r{x to the power of 3 }
f A LaTex expression showing 1 over xsquare root of r{x 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 {m} to the power of -5 over 2 times {c} to the power of -3 over 2
a A LaTex expression showing 1 over 2mcsquare root of 3{m to the power of 2{c to the power of 3 }}
b A LaTex expression showing 1 over square root of 2{m to the power of 5{c to the power of 3 }}
c A LaTex expression showing 1 over {m to the power of 2 csquare root of 4{m to the power of 3 c}}
d A LaTex expression showing 1 over {m to the power of 4 {c} to the power of 3 square root of m{c to the power of 3 }}
e A LaTex expression showing 1 over mcsquare root of mc
f A LaTex expression showing 1 over 3mcsquare root of 3mc
4
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {c} to the power of -3 over 2 times n to the power of -1 over 2
a A LaTex expression showing 1 over 4csquare root of {c to the power of 3n }
b A LaTex expression showing 1 over square root of 3{c to the power of 3n }
c A LaTex expression showing 1 over 2csquare root of 2c{n to the power of 2 }
d A LaTex expression showing 1 over {c to the power of 3 square root of 2cn}
e A LaTex expression showing 1 over {c to the power of 2 square root of 3{c to the power of 2 n}}
f A LaTex expression showing 1 over {c to the power of 2 square root of {c to the power of 3 n}}
5
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {y} to the power of -5 over 2 times {d} to the power of -5 over 2
a A LaTex expression showing 1 over {y to the power of 2 {d} to the power of 4 square root of y{d to the power of 3 }}
b A LaTex expression showing 1 over 4{y to the power of 2 {d} to the power of 4 square root of yd}
c A LaTex expression showing 1 over 4y{d to the power of 3 square root of y{d to the power of 2 }}
d A LaTex expression showing 1 over {y to the power of 3 dsquare root of 3{y to the power of 2 {d} to the power of 3 }}
e A LaTex expression showing 1 over square root of 3{y to the power of 5{d to the power of 5 }}
f A LaTex expression showing 1 over {y to the power of 2 {d} to the power of 3 square root of 6y{d to the power of 2 }}
6
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 zmsquare root of 8zm
b A LaTex expression showing 1 over 2zmsquare root of 7{z to the power of 3m }
c A LaTex expression showing 1 over 4{z to the power of 2 msquare root of 5zm}
d 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 }}
e A LaTex expression showing 1 over z{m to the power of 3 square root of 5zm}
f A LaTex expression showing 1 over square root of 5{z to the power of 3{m to the power of 3 }}
7
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {c} to the power of -3 over 2 times {d} to the power of -3 over 2
a A LaTex expression showing 1 over 4cdsquare root of 4{c to the power of 2d }
b A LaTex expression showing 1 over c{d to the power of 3 square root of 3c{d to the power of 3 }}
c A LaTex expression showing 1 over square root of 3{c to the power of 3{d to the power of 3 }}
d A LaTex expression showing 1 over {c to the power of 2 dsquare root of {c to the power of 3 d}}
e A LaTex expression showing 1 over 3cdsquare root of cd
f A LaTex expression showing 1 over c{d to the power of 2 square root of cd}