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

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Radicals - Convert Square Root, Values and Variables, from Exponents - Negative
1
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times d to the power of -1 over 2
a A LaTex expression showing 1 over 4square root of d
b A LaTex expression showing 1 over square root of 3d
c A LaTex expression showing 1 over square root of d
d A LaTex expression showing 1 over square root of 2d
e A LaTex expression showing square root of d
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
a A LaTex expression showing 1 over square root of 2r
b A LaTex expression showing 1 over 2square root of 2r
c A LaTex expression showing 1 over 2square root of r
d A LaTex expression showing square root of r
3
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 2 times x to the power of -1 over 2
a A LaTex expression showing 1 over 2square root of 9x
b A LaTex expression showing 1 over square root of 10{x to the power of 2 }
c A LaTex expression showing 1 over square root of 11x
d A LaTex expression showing 2square root of 12x
e A LaTex expression showing 1 over square root of 14x
4
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 3{m to the power of 2 }
b A LaTex expression showing 1 over 3msquare root of {m to the power of 2 }
c A LaTex expression showing 1 over msquare root of 6{m to the power of 2 }
d A LaTex expression showing 1 over square root of 3{m to the power of 3 }
e A LaTex expression showing {m} to the power of 3 square root of 4{m to the power of 2 }
5
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of -1 over 2 times {m} to the power of -3 over 2
a A LaTex expression showing 1 over 4msquare root of 11{m to the power of 2 }
b A LaTex expression showing 1 over msquare root of 8m
c A LaTex expression showing 1 over 2msquare root of 13{m to the power of 3 }
d A LaTex expression showing 1 over square root of 11{m to the power of 3 }
e A LaTex expression showing 4msquare root of 10m
6
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 {d to the power of 2 square root of d}
b A LaTex expression showing 1 over 3{d to the power of 2 square root of 3{d to the power of 2 }}
c A LaTex expression showing {d} to the power of 3 square root of d
d A LaTex expression showing 1 over dsquare root of d
e A LaTex expression showing 1 over square root of 3{d to the power of 3 }
7
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 2 times m to the power of -1 over 2
a A LaTex expression showing square root of 10m
b A LaTex expression showing 1 over square root of 4m
c A LaTex expression showing 1 over square root of 7m
d A LaTex expression showing 1 over square root of 3{m to the power of 3 }
e A LaTex expression showing 1 over 3square root of 8{m to the power of 3 }
8
Convert the fractional exponent to a radical
A LaTex expression showing 7 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 4x}
b A LaTex expression showing 1 over {x to the power of 3 square root of 8{x to the power of 3 }}
c A LaTex expression showing xsquare root of 5{x to the power of 3 }
d A LaTex expression showing 1 over square root of 7{x to the power of 3 }
e A LaTex expression showing 1 over xsquare root of 9x