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

This math topic focuses on converting fractional exponents to radicals, which involves simplifying expressions that contain negative exponents. The problems require knowledge of how to handle powers and roots, particularly in the context of variables and constants. Each problem presents a mathematical expression with variables raised to negative fractional powers, and the student must convert these into radical form, choosing the correct option among multiple answers. This practice is part of a broader unit on simplifying radicals, enhancing problem-solving skills related to algebraic manipulation and exponent rules.

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 - Negative Worksheet

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Radicals - Convert Square Root, Values and Variables, from Exponents - Negative
1
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 -5 over 2 times {p} to the power of -3 over 2
a A LaTex expression showing {r} to the power of 3 psquare root of 6{r to the power of 3 p}
b A LaTex expression showing 1 over 2{r to the power of 2 {p} to the power of 2 square root of 7r{p to the power of 2 }}
c A LaTex expression showing 1 over square root of 7{r to the power of 5{p to the power of 3 }}
d A LaTex expression showing 1 over rpsquare root of 8rp
e A LaTex expression showing 1 over {r to the power of 3 {p} to the power of 3 square root of 9{r to the power of 2 p}}
2
Convert the fractional exponent to a radical
A LaTex expression showing 7 to the power of -1 over 2 times {x} to the power of -5 over 2 times p to the power of -1 over 2
a A LaTex expression showing 1 over {x to the power of 2 square root of 3x{p to the power of 2 }}
b A LaTex expression showing 1 over 3{x to the power of 3 square root of 8xp}
c A LaTex expression showing 1 over 3xsquare root of 7x{p to the power of 2 }
d A LaTex expression showing xsquare root of 10xp
e A LaTex expression showing 1 over square root of 7{x to the power of 5p }
3
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {c} to the power of -3 over 2 times p to the power of -1 over 2
a A LaTex expression showing 1 over square root of 3{c to the power of 3p }
b A LaTex expression showing 3csquare root of 2{c to the power of 3 {p} to the power of 2 }
c A LaTex expression showing 1 over {c to the power of 3 square root of c{p to the power of 3 }}
d A LaTex expression showing 1 over csquare root of 3c{p to the power of 2 }
e A LaTex expression showing 1 over csquare root of c{p 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 {y} to the power of -3 over 2 times {z} to the power of -3 over 2
a A LaTex expression showing 1 over y{z to the power of 3 square root of 10y{z to the power of 2 }}
b A LaTex expression showing 1 over 2yzsquare root of 9{y to the power of 3{z to the power of 3 }}
c A LaTex expression showing 1 over y{z to the power of 2 square root of 8yz}
d A LaTex expression showing 1 over square root of 7{y to the power of 3{z to the power of 3 }}
e A LaTex expression showing yzsquare root of 8{y to the power of 2 z}
5
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {p} to the power of -3 over 2 times b to the power of -1 over 2
a A LaTex expression showing 1 over square root of 3{p to the power of 3b }
b A LaTex expression showing {p} to the power of 3 square root of 5p{b to the power of 3 }
c A LaTex expression showing 1 over 2{p to the power of 2 square root of 3{p to the power of 2 b}}
d A LaTex expression showing 1 over {p to the power of 2 square root of 2pb}
e A LaTex expression showing 1 over psquare root of 6{p to the power of 2b }
6
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 -1 over 2 times {n} to the power of -5 over 2
a A LaTex expression showing 1 over {n to the power of 4 square root of bn}
b A LaTex expression showing 1 over {n to the power of 4 square root of b{n to the power of 2 }}
c A LaTex expression showing 1 over {n to the power of 3 square root of 2{b to the power of 2 {n} to the power of 3 }}
d A LaTex expression showing 1 over square root of 2b{n to the power of 5 }
e A LaTex expression showing 4{n} to the power of 3 square root of 4b{n 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 {p} to the power of -5 over 2 times {y} to the power of -3 over 2
a A LaTex expression showing 1 over {p to the power of 2 {y} to the power of 3 square root of p{y to the power of 3 }}
b A LaTex expression showing 1 over square root of 2{p to the power of 5{y to the power of 3 }}
c A LaTex expression showing 1 over 2{p to the power of 2 {y} to the power of 2 square root of {p to the power of 2 y}}
d A LaTex expression showing {p} to the power of 3 ysquare root of {p to the power of 3 y}
e A LaTex expression showing 1 over pysquare root of 5p{y to the power of 3 }
8
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 {b} to the power of -3 over 2
a A LaTex expression showing 1 over square root of 7{y to the power of 5{b to the power of 3 }}
b A LaTex expression showing 1 over 2ybsquare root of 7{y to the power of 3b }
c A LaTex expression showing 1 over ybsquare root of 7{y to the power of 3{b to the power of 3 }}
d A LaTex expression showing 1 over ybsquare root of 9{y to the power of 2{b to the power of 2 }}
e A LaTex expression showing 3{y} to the power of 2 bsquare root of 7yb