Radical

Convert Square Root, Values and Variables, from Exponents - Negative (Level 1)

This math topic focuses on converting fractional exponents to radicals, particularly when the exponents are negative. The problems involve both numerical values and variables, requiring students to manipulate and simplify expressions with square roots and powers. The level of complexity is introductory, as part of a broader unit on simplifying radicals. Each problem includes multiple-choice answers, requiring the learner to determine the correct radical form of given expressions. This topic is part of a series aimed at developing skills in handling radicals and understanding their relationship with exponents.

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

more
View Unit

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

212b322^{-\frac{1}{2}}\cdot {b}^{-\frac{3}{2}}

?

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

Mobius Math Club logo
Math worksheet on 'Radicals - Convert Square Root, Values and Variables, from Exponents - Negative (Level 1)'. 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 {z} to the power of -3 over 2
a A LaTex expression showing 1 over {z to the power of 3 square root of {z to the power of 2 }}
b A LaTex expression showing 1 over 3zsquare root of 2{z to the power of 3 }
c A LaTex expression showing 1 over 2{z to the power of 2 square root of z}
d A LaTex expression showing 1 over zsquare root of 2z
e A LaTex expression showing 1 over square root of 2{z to the power of 3 }
f A LaTex expression showing 1 over 3zsquare root of 4{z to the power of 3 }
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 2 times {b} to the power of -3 over 2
a A LaTex expression showing 1 over 3{b to the power of 3 square root of 3b}
b A LaTex expression showing 1 over 3{b to the power of 2 square root of 5b}
c A LaTex expression showing 1 over {b to the power of 2 square root of 3b}
d A LaTex expression showing 1 over square root of 7{b to the power of 3 }
e A LaTex expression showing 1 over {b to the power of 3 square root of 4b}
f A LaTex expression showing 1 over 2bsquare root of 4b
3
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times x to the power of -1 over 2
a A LaTex expression showing 1 over square root of 2x
b A LaTex expression showing 1 over 4square root of 4x
c A LaTex expression showing 1 over 4square root of x
d A LaTex expression showing 1 over 2square root of 2x
e A LaTex expression showing 1 over square root of 5x
f A LaTex expression showing 1 over square root of x
4
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 2 times {n} to the power of -3 over 2
a A LaTex expression showing 1 over {n to the power of 3 square root of 14n}
b A LaTex expression showing 1 over square root of 11{n to the power of 3 }
c A LaTex expression showing 1 over {n to the power of 2 square root of 7{n to the power of 2 }}
d A LaTex expression showing 1 over nsquare root of 10n
e A LaTex expression showing 1 over {n to the power of 3 square root of 9{n to the power of 3 }}
f A LaTex expression showing 1 over nsquare root of 7n
5
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 2 times n to the power of -1 over 2
a A LaTex expression showing 1 over square root of 5{n to the power of 2 }
b A LaTex expression showing 1 over 4square root of 5n
c A LaTex expression showing 1 over square root of 8{n to the power of 2 }
d A LaTex expression showing 1 over 3square root of 7n
e A LaTex expression showing 1 over 2square root of 10n
f A LaTex expression showing 1 over square root of 7n
6
Convert the fractional exponent to a radical
A LaTex expression showing 3 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 4{m to the power of 3 }
b A LaTex expression showing 1 over 3msquare root of 2m
c A LaTex expression showing 1 over square root of 3{m to the power of 3 }
d A LaTex expression showing 1 over msquare root of 2{m to the power of 2 }
e A LaTex expression showing 1 over 2{m to the power of 3 square root of 4m}
f A LaTex expression showing 1 over msquare root of 3{m to the power of 3 }
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 -3 over 2
a A LaTex expression showing 1 over {m to the power of 2 square root of m}
b A LaTex expression showing 1 over {m to the power of 3 square root of 3m}
c A LaTex expression showing 1 over 2{m to the power of 2 square root of 3m}
d A LaTex expression showing 1 over square root of 5{m to the power of 3 }
e A LaTex expression showing 1 over 4msquare root of 5m
f A LaTex expression showing 1 over msquare root of 6m