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Radicals - Convert Square Root, Values and Variables, from Exponents - Positive (Level 2)

This math topic focuses on converting expressions with fractional exponents into radical form. It addresses combinations of numerical coefficients and variables raised to positive fractional powers. Each question provides an expression for conversion, testing the student's ability to apply the rules of exponents and radicals. The multiple-choice format assesses understanding by selecting the correct radical form among several options. This is part of a broader unit on simplifying radicals, enhancing skills crucial for algebra and advanced mathematics.

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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Convert the fractional exponent to a radical

312⋅z32⋅n523^{\frac{1}{2}}\cdot {z}^{\frac{3}{2}}\cdot {n}^{\frac{5}{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 2)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 2 times m to the power of 1 over 2 times b to the power of 1 over 2
a A LaTex expression showing square root of mb
b A LaTex expression showing 2square root of 5mb
c A LaTex expression showing square root of 5mb
d A LaTex expression showing square root of 2mb
e A LaTex expression showing square root of 3{m to the power of 3 {b} to the power of 3 }
f A LaTex expression showing 2square root of m{b to the power of 3 }
2
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 5 over 2 times {b} to the power of 3 over 2
a A LaTex expression showing 4ybsquare root of {y to the power of 3 {b} to the power of 3 }
b A LaTex expression showing 4y{b} to the power of 3 square root of 6{y to the power of 2 b}
c A LaTex expression showing {y} to the power of 4 {b} to the power of 3 square root of 3yb
d A LaTex expression showing square root of 3{y to the power of 5 {b} to the power of 3 }
e A LaTex expression showing {y} to the power of 3 bsquare root of 3yb
f A LaTex expression showing y{b} to the power of 2 square root of 5{y to the power of 3 b}
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 times {d} to the power of 3 over 2
a A LaTex expression showing {b} to the power of 3 dsquare root of 6bd
b A LaTex expression showing square root of 7{b to the power of 3 {d} to the power of 3 }
c A LaTex expression showing b{d} to the power of 3 square root of 5bd
d A LaTex expression showing 2{b} to the power of 3 {d} to the power of 2 square root of 10bd
e A LaTex expression showing {b} to the power of 3 {d} to the power of 2 square root of 8{b to the power of 3 d}
f A LaTex expression showing bdsquare root of 3{b to the power of 3 {d} to the power of 3 }
4
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 times {c} to the power of 3 over 2
a A LaTex expression showing csquare root of 11n{c to the power of 2 }
b A LaTex expression showing csquare root of 14n{c to the power of 2 }
c A LaTex expression showing 3{c} to the power of 3 square root of 7nc
d A LaTex expression showing 2csquare root of 13{n to the power of 3 {c} to the power of 2 }
e A LaTex expression showing square root of 11n{c to the power of 3 }
f A LaTex expression showing csquare root of 10n{c 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 {n} to the power of 5 over 2 times {c} to the power of 3 over 2
a A LaTex expression showing n{c} to the power of 2 square root of 12{n to the power of 2 c}
b A LaTex expression showing 4{n} to the power of 3 csquare root of 10{n to the power of 2 c}
c A LaTex expression showing 4ncsquare root of 9nc
d A LaTex expression showing ncsquare root of 8n{c to the power of 2 }
e A LaTex expression showing {n} to the power of 3 {c} to the power of 3 square root of 8n{c to the power of 2 }
f A LaTex expression showing square root of 11{n to the power of 5 {c} to the power of 3 }
6
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 2 times {n} to the power of 5 over 2 times y to the power of 1 over 2
a A LaTex expression showing square root of 5{n to the power of 5 y}
b A LaTex expression showing nsquare root of 2{n to the power of 3 {y} to the power of 3 }
c A LaTex expression showing 2nsquare root of {n to the power of 2 {y} to the power of 2 }
d A LaTex expression showing 3nsquare root of 6n{y to the power of 3 }
e A LaTex expression showing 3{n} to the power of 4 square root of 2ny
f A LaTex expression showing nsquare root of 4{n to the power of 3 y}
7
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 2 times {d} to the power of 3 over 2 times {n} to the power of 5 over 2
a A LaTex expression showing {d} to the power of 3 {n} to the power of 3 square root of 4{d to the power of 3 {n} to the power of 3 }
b A LaTex expression showing d{n} to the power of 2 square root of 8dn
c A LaTex expression showing 4d{n} to the power of 3 square root of 5{d to the power of 3 n}
d A LaTex expression showing square root of 7{d to the power of 3 {n} to the power of 5 }
e A LaTex expression showing dnsquare root of 4d{n to the power of 3 }
f A LaTex expression showing {d} to the power of 3 {n} to the power of 3 square root of 10d{n to the power of 2 }