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Radicals - 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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Convert Square Root, Values and Variables, from Exponents - Positive

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Convert the fractional exponent to a radical

1112â‹…d3211^{\frac{1}{2}}\cdot {d}^{\frac{3}{2}}

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

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Math worksheet on 'Radicals - Convert Square Root, Values and Variables, from Exponents - Positive (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 3 to the power of 1 over 2 times {p} to the power of 3 over 2
a A LaTex expression showing 3{p} to the power of 3 square root of 2p
b A LaTex expression showing psquare root of 2p
c A LaTex expression showing square root of 3{p to the power of 3 }
d A LaTex expression showing psquare root of {p to the power of 2 }
e A LaTex expression showing {p} to the power of 3 square root of 3{p to the power of 2 }
f A LaTex expression showing psquare root of p
2
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 2 times c to the power of 1 over 2
a A LaTex expression showing square root of 7c
b A LaTex expression showing 2square root of 10c
c A LaTex expression showing square root of 11{c to the power of 3 }
d A LaTex expression showing square root of 8{c to the power of 2 }
e A LaTex expression showing square root of 10c
f A LaTex expression showing square root of 11c
3
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 4square root of 14n
b A LaTex expression showing square root of 13n
c A LaTex expression showing square root of 11n
d A LaTex expression showing 4square root of 11{n to the power of 2 }
e A LaTex expression showing 4square root of 7{n to the power of 3 }
f A LaTex expression showing square root of 13{n to the power of 3 }
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 xsquare root of 9{x to the power of 2 }
b A LaTex expression showing 3{x} to the power of 2 square root of 8x
c A LaTex expression showing square root of 7{x to the power of 3 }
d A LaTex expression showing 4{x} to the power of 2 square root of 6x
e A LaTex expression showing xsquare root of 6x
f A LaTex expression showing 3xsquare root of 8x
5
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 2 times p to the power of 1 over 2
a A LaTex expression showing square root of 3{p to the power of 3 }
b A LaTex expression showing square root of 2p
c A LaTex expression showing square root of p
d A LaTex expression showing 4square root of 4p
e A LaTex expression showing square root of 5p
f A LaTex expression showing square root of 2{p to the power of 3 }
6
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 1 over 2
a A LaTex expression showing 3square root of 2y
b A LaTex expression showing square root of y
c A LaTex expression showing square root of 5{y to the power of 3 }
d A LaTex expression showing 3square root of y
e A LaTex expression showing 3square root of 4{y to the power of 3 }
f A LaTex expression showing square root of 3y
7
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 2 times b to the power of 1 over 2
a A LaTex expression showing square root of 11b
b A LaTex expression showing square root of 10b
c A LaTex expression showing square root of 9b
d A LaTex expression showing square root of 13b
e A LaTex expression showing square root of 7b
f A LaTex expression showing 2square root of 14{b to the power of 3 }