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Radicals - 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.

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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

7−12⋅y−327^{-\frac{1}{2}}\cdot {y}^{-\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 1)'. Part of a broader unit on 'Radicals - Simplifying Intro' Learn online: app.mobius.academy/math/units/radicals_simplifying_intro/
1
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {p} to the power of -3 over 2
a A LaTex expression showing 1 over square root of 5{p to the power of 3 }
b A LaTex expression showing 1 over {p to the power of 2 square root of 5p}
c A LaTex expression showing 1 over psquare root of p
d A LaTex expression showing 1 over psquare root of 7{p to the power of 3 }
e A LaTex expression showing 1 over 3psquare root of 7p
f A LaTex expression showing 1 over 3{p to the power of 3 square root of 5p}
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 2 times c to the power of -1 over 2
a A LaTex expression showing 1 over square root of 6c
b A LaTex expression showing 1 over square root of 9{c to the power of 3 }
c A LaTex expression showing 1 over square root of 4c
d A LaTex expression showing 1 over square root of 10c
e A LaTex expression showing 1 over square root of 7c
f A LaTex expression showing 1 over 4square root of 10c
3
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 -1 over 2
a A LaTex expression showing 1 over 2square root of 9b
b A LaTex expression showing 1 over square root of 7{b to the power of 3 }
c A LaTex expression showing 1 over square root of 9b
d A LaTex expression showing 1 over square root of 7b
e A LaTex expression showing 1 over 3square root of 5b
f A LaTex expression showing 1 over 4square root of 7b
4
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 square root of 8{n to the power of 2 }
c A LaTex expression showing 1 over square root of 7n
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 4square root of 5n
5
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 -1 over 2
a A LaTex expression showing 1 over 3square root of y
b A LaTex expression showing 1 over square root of {y to the power of 2 }
c A LaTex expression showing 1 over square root of 5y
d A LaTex expression showing 1 over 4square root of 4{y to the power of 3 }
e A LaTex expression showing 1 over square root of y
f A LaTex expression showing 1 over square root of 2y
6
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {y} to the power of -3 over 2
a A LaTex expression showing 1 over ysquare root of 3y
b A LaTex expression showing 1 over {y to the power of 3 square root of 4y}
c A LaTex expression showing 1 over {y to the power of 3 square root of 2y}
d A LaTex expression showing 1 over 3ysquare root of 5y
e A LaTex expression showing 1 over square root of 5{y to the power of 3 }
f A LaTex expression showing 1 over 2ysquare root of 4y
7
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {d} to the power of -3 over 2
a A LaTex expression showing 1 over square root of 3{d to the power of 3 }
b A LaTex expression showing 1 over 3dsquare root of 5d
c A LaTex expression showing 1 over dsquare root of 2d
d A LaTex expression showing 1 over 4dsquare root of 2d
e A LaTex expression showing 1 over dsquare root of 2{d to the power of 3 }
f A LaTex expression showing 1 over 4dsquare root of d