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

This math topic focuses on converting fractional exponents to radicals. It is part of a broader introductory unit on simplifying radicals. Each question presents expressions with fractional exponents involving numbers and variables, asking students to rewrite them in radical form. Various options for the answers suggest multiple ways these exponents can be represented as radicals, emphasizing understanding of radical simplification and conversion between different forms of expressing mathematical power. This set of problems is beneficial for students learning to manipulate and simplify expressions involving powers and roots.

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 - Positive Worksheet

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