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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.

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

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Convert the fractional exponent to a radical

512â‹…c32â‹…x125^{\frac{1}{2}}\cdot {c}^{\frac{3}{2}}\cdot x^{\frac{1}{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 {c} to the power of 3 over 2 times {y} to the power of 3 over 2
a A LaTex expression showing cysquare root of cy
b A LaTex expression showing square root of 5{c to the power of 3 {y} to the power of 3 }
c A LaTex expression showing cysquare root of 6cy
d A LaTex expression showing 3{c} to the power of 3 ysquare root of 6{c to the power of 3 y}
e A LaTex expression showing {c} to the power of 2 ysquare root of 8cy
f A LaTex expression showing 2{c} to the power of 3 ysquare root of 5cy
2
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 2 times {b} to the power of 3 over 2 times m to the power of 1 over 2
a A LaTex expression showing bsquare root of 5b{m to the power of 2 }
b A LaTex expression showing bsquare root of bm
c A LaTex expression showing 4bsquare root of 4{b to the power of 2 {m} to the power of 2 }
d A LaTex expression showing 2{b} to the power of 3 square root of 2bm
e A LaTex expression showing 3{b} to the power of 3 square root of 3{b to the power of 3 m}
f A LaTex expression showing square root of 2{b to the power of 3 m}
3
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 2 times {z} to the power of 5 over 2 times c to the power of 1 over 2
a A LaTex expression showing square root of 2{z to the power of 5 c}
b A LaTex expression showing {z} to the power of 3 square root of {z to the power of 2 c}
c A LaTex expression showing {z} to the power of 2 square root of 4{z to the power of 2 c}
d A LaTex expression showing 4zsquare root of {z to the power of 3 {c} to the power of 2 }
e A LaTex expression showing {z} to the power of 2 square root of {z to the power of 3 {c} to the power of 3 }
f A LaTex expression showing {z} to the power of 4 square root of z{c to the power of 2 }
4
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 10d{n to the power of 2 }
b A LaTex expression showing d{n} to the power of 2 square root of 8dn
c 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 }
d A LaTex expression showing 4d{n} to the power of 3 square root of 5{d to the power of 3 n}
e A LaTex expression showing square root of 7{d to the power of 3 {n} to the power of 5 }
f A LaTex expression showing dnsquare root of 4d{n to the power of 3 }
5
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of 1 over 2 times p to the power of 1 over 2 times {z} to the power of 3 over 2
a A LaTex expression showing 3zsquare root of 6pz
b A LaTex expression showing {z} to the power of 2 square root of 5{p to the power of 3 z}
c A LaTex expression showing 2{z} to the power of 2 square root of 8p{z to the power of 3 }
d A LaTex expression showing 2{z} to the power of 2 square root of pz
e A LaTex expression showing square root of 5p{z to the power of 3 }
f A LaTex expression showing {z} to the power of 3 square root of 2{p to the power of 3 {z} 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 {d} to the power of 5 over 2 times {y} to the power of 5 over 2
a A LaTex expression showing square root of 5{d to the power of 5 {y} to the power of 5 }
b A LaTex expression showing dysquare root of 2d{y to the power of 3 }
c A LaTex expression showing d{y} to the power of 3 square root of dy
d A LaTex expression showing 2{d} to the power of 3 ysquare root of 8dy
e A LaTex expression showing {d} to the power of 4 {y} to the power of 2 square root of 7dy
f A LaTex expression showing 4{d} to the power of 3 {y} to the power of 4 square root of 8dy
7
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 2 times {z} to the power of 5 over 2 times {b} to the power of 3 over 2
a A LaTex expression showing {z} to the power of 2 {b} to the power of 2 square root of 4z{b to the power of 2 }
b A LaTex expression showing 3{z} to the power of 3 bsquare root of 10{z to the power of 2 b}
c A LaTex expression showing {z} to the power of 3 bsquare root of 5{z to the power of 2 {b} to the power of 3 }
d A LaTex expression showing square root of 7{z to the power of 5 {b} to the power of 3 }
e A LaTex expression showing 3{z} to the power of 2 bsquare root of 7{z to the power of 2 b}
f A LaTex expression showing {z} to the power of 3 {b} to the power of 3 square root of 3z{b to the power of 2 }