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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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 Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 2 times {y} to the power of 5 over 2 times {p} to the power of 3 over 2
a A LaTex expression showing {y} to the power of 3 {p} to the power of 3 square root of 8{y to the power of 3 {p} to the power of 3 }
b A LaTex expression showing square root of 11{y to the power of 5 {p} to the power of 3 }
c A LaTex expression showing 3{y} to the power of 3 {p} to the power of 2 square root of 8{y to the power of 2 {p} to the power of 3 }
d A LaTex expression showing 1 over {y to the power of 4 {p} to the power of 2 square root of 14yp}
e A LaTex expression showing 4{y} to the power of 4 psquare root of 10{y to the power of 3 {p} to the power of 2 }
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 5 over 2 times {y} to the power of 3 over 2
a A LaTex expression showing z{y} to the power of 2 square root of 7{z to the power of 3 y}
b A LaTex expression showing square root of 5{z to the power of 5 {y} to the power of 3 }
c A LaTex expression showing 4{z} to the power of 4 {y} to the power of 2 square root of 6z{y to the power of 3 }
d A LaTex expression showing 1 over {z to the power of 4 {y} to the power of 2 square root of 3z{y to the power of 2 }}
e A LaTex expression showing 4{z} to the power of 2 ysquare root of 6zy
3
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 times {z} to the power of 5 over 2
a A LaTex expression showing 1 over zsquare root of 14bz
b A LaTex expression showing zsquare root of 13{b to the power of 2 z}
c A LaTex expression showing zsquare root of 7bz
d A LaTex expression showing square root of 11b{z to the power of 5 }
e A LaTex expression showing 4zsquare root of 11{b to the power of 2 {z} to the power of 2 }
4
Convert the fractional exponent to a radical
A LaTex expression showing 11 to the power of 1 over 2 times {y} to the power of 3 over 2 times {x} to the power of 5 over 2
a A LaTex expression showing 1 over {y to the power of 3 {x} to the power of 4 square root of 7y{x to the power of 2 }}
b A LaTex expression showing square root of 11{y to the power of 3 {x} to the power of 5 }
c A LaTex expression showing 3{y} to the power of 2 {x} to the power of 3 square root of 9yx
d A LaTex expression showing 4{y} to the power of 3 xsquare root of 7yx
e A LaTex expression showing 4y{x} to the power of 2 square root of 13y{x 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 {x} to the power of 3 over 2 times {n} to the power of 5 over 2
a A LaTex expression showing square root of 5{x to the power of 3 {n} to the power of 5 }
b A LaTex expression showing 3{x} to the power of 3 {n} to the power of 3 square root of xn
c A LaTex expression showing xnsquare root of {x to the power of 2 n}
d A LaTex expression showing {x} to the power of 3 nsquare root of 8{x to the power of 2 {n} to the power of 3 }
e A LaTex expression showing 1 over 2{x to the power of 3 nsquare root of 2xn}
6
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 2 times {m} to the power of 5 over 2 times r to the power of 1 over 2
a A LaTex expression showing {m} to the power of 3 square root of 4m{r to the power of 3 }
b A LaTex expression showing 1 over 2{m to the power of 2 square root of {m to the power of 2 r}}
c A LaTex expression showing {m} to the power of 2 square root of {m to the power of 3 {r} to the power of 3 }
d A LaTex expression showing 2{m} to the power of 3 square root of m{r to the power of 3 }
e A LaTex expression showing square root of 2{m to the power of 5 r}
7
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 3 over 2 times d to the power of 1 over 2
a A LaTex expression showing 1 over 4ysquare root of 5y{d to the power of 2 }
b A LaTex expression showing 2{y} to the power of 3 square root of {y to the power of 3 d}
c A LaTex expression showing square root of 3{y to the power of 3 d}
d A LaTex expression showing 4ysquare root of 3y{d to the power of 2 }
e A LaTex expression showing ysquare root of 3yd
Radicals - Convert Square Root, Values and Variables, from Exponents - Positive (Level 2) - Mobius Math