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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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 11 to the power of 1 over 2 times {n} to the power of 3 over 2
a A LaTex expression showing 1 over 2nsquare root of 11{n to the power of 3 }
b A LaTex expression showing nsquare root of 9{n to the power of 2 }
c A LaTex expression showing nsquare root of 8{n to the power of 2 }
d A LaTex expression showing square root of 11{n to the power of 3 }
e A LaTex expression showing 4{n} to the power of 2 square root of 13n
2
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 2 times z to the power of 1 over 2
a A LaTex expression showing 3square root of z
b A LaTex expression showing 1 over square root of 7z
c A LaTex expression showing square root of 4{z to the power of 3 }
d A LaTex expression showing square root of z
e A LaTex expression showing square root of 5z
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 3 over 2
a A LaTex expression showing bsquare root of 10{b to the power of 2 }
b A LaTex expression showing bsquare root of 4b
c A LaTex expression showing 4bsquare root of 7b
d A LaTex expression showing 1 over bsquare root of 4b
e A LaTex expression showing square root of 7{b to the power of 3 }
4
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 {d to the power of 3 }
b A LaTex expression showing 1 over 4square root of 4{d to the power of 2 }
c A LaTex expression showing square root of 4{d to the power of 2 }
d A LaTex expression showing square root of d
e A LaTex expression showing square root of 2d
5
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 3x
c A LaTex expression showing square root of x
d A LaTex expression showing square root of {x to the power of 2 }
e A LaTex expression showing 1 over 2square root of 3x
6
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of 1 over 2 times z to the power of 1 over 2
a A LaTex expression showing square root of 2z
b A LaTex expression showing 2square root of z
c A LaTex expression showing square root of 3z
d A LaTex expression showing 1 over 3square root of 4z
e A LaTex expression showing 3square root of 3z
7
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 3 over 2
a A LaTex expression showing {x} to the power of 2 square root of 8x
b A LaTex expression showing 1 over 4xsquare root of 7x
c A LaTex expression showing 4{x} to the power of 2 square root of 7{x to the power of 3 }
d A LaTex expression showing 2xsquare root of 7x
e A LaTex expression showing square root of 5{x to the power of 3 }
Radicals - Convert Square Root, Values and Variables, from Exponents - Positive (Level 1) - Mobius Math Academy