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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Radicals - Convert Square Root, Values and Variables, from Exponents - Positive
1
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of 1 over 2 times {x} to the power of 5 over 2 times {m} to the power of 3 over 2
a A LaTex expression showing 4xmsquare root of {x to the power of 3 m}
b A LaTex expression showing {x} to the power of 2 {m} to the power of 3 square root of 5x{m to the power of 3 }
c A LaTex expression showing 1 over {x to the power of 2 msquare root of 5{x to the power of 3 m}}
d A LaTex expression showing square root of 2{x to the power of 5 {m} to the power of 3 }
e A LaTex expression showing 2{x} to the power of 3 msquare root of xm
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 2 times {r} to the power of 3 over 2 times {b} to the power of 3 over 2
a A LaTex expression showing rbsquare root of 3rb
b A LaTex expression showing 1 over r{b to the power of 2 square root of 7{r to the power of 2 b}}
c A LaTex expression showing {r} to the power of 2 bsquare root of 5rb
d A LaTex expression showing square root of 7{r to the power of 3 {b} to the power of 3 }
e A LaTex expression showing {r} to the power of 2 {b} to the power of 3 square root of 8{r to the power of 2 {b} to the power of 3 }
3
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 2 times {y} to the power of 5 over 2 times d to the power of 1 over 2
a A LaTex expression showing 1 over 2{y to the power of 2 square root of 9y{d to the power of 2 }}
b A LaTex expression showing 3{y} to the power of 4 square root of 7yd
c A LaTex expression showing ysquare root of 5{y to the power of 2 {d} to the power of 2 }
d A LaTex expression showing square root of 7{y to the power of 5 d}
e A LaTex expression showing ysquare root of 7{y to the power of 2 d}
4
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 {x} to the power of 3 nsquare root of 8{x to the power of 2 {n} to the power of 3 }
b A LaTex expression showing xnsquare root of {x to the power of 2 n}
c A LaTex expression showing 1 over 2{x to the power of 3 nsquare root of 2xn}
d A LaTex expression showing 3{x} to the power of 3 {n} to the power of 3 square root of xn
e A LaTex expression showing square root of 5{x to the power of 3 {n} to the power of 5 }
5
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of 1 over 2 times y to the power of 1 over 2 times r to the power of 1 over 2
a A LaTex expression showing 1 over square root of 7yr
b A LaTex expression showing square root of 5{y to the power of 2 r}
c A LaTex expression showing square root of 7yr
d A LaTex expression showing 1 over 3square root of 3{y to the power of 3{r to the power of 3 }}
e A LaTex expression showing 2square root of 6y{r to the power of 3 }
6
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 {y} to the power of 5 over 2
a A LaTex expression showing 1 over d{y to the power of 4 square root of 8{d to the power of 3 y}}
b A LaTex expression showing d{y} to the power of 3 square root of 5{d to the power of 3 {y} to the power of 2 }
c A LaTex expression showing square root of 7{d to the power of 3 {y} to the power of 5 }
d A LaTex expression showing d{y} to the power of 4 square root of 6{d to the power of 2 y}
e A LaTex expression showing d{y} to the power of 4 square root of 10d{y to the power of 2 }
7
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 2 square root of {m to the power of 3 {r} to the power of 3 }
b A LaTex expression showing square root of 2{m to the power of 5 r}
c A LaTex expression showing {m} to the power of 3 square root of 4m{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 1 over 2{m to the power of 2 square root of {m to the power of 2 r}}
8
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 z to the power of 1 over 2
a A LaTex expression showing 4dsquare root of 6d{z to the power of 3 }
b A LaTex expression showing square root of 7{d to the power of 3 z}
c A LaTex expression showing 2dsquare root of 9dz
d A LaTex expression showing 4{d} to the power of 3 square root of 9d{z to the power of 2 }
e A LaTex expression showing 1 over {d to the power of 2 square root of 9{d to the power of 2 {z} to the power of 3 }}