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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Math worksheet on 'Radicals - Convert Square Root, Values and Variables, from Exponents - Negative (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 7 to the power of -1 over 2 times {r} to the power of -5 over 2 times b to the power of -1 over 2
a A LaTex expression showing rsquare root of 10{r to the power of 3 {b} to the power of 2 }
b A LaTex expression showing 1 over {r to the power of 4 square root of 10rb}
c A LaTex expression showing 1 over square root of 7{r to the power of 5b }
d A LaTex expression showing 1 over 2{r to the power of 2 square root of 5{r to the power of 2 {b} to the power of 2 }}
e A LaTex expression showing 1 over 3rsquare root of 5r{b to the power of 2 }
2
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 -3 over 2 times c to the power of -1 over 2
a A LaTex expression showing 1 over bsquare root of 7bc
b A LaTex expression showing 1 over bsquare root of 11b{c to the power of 2 }
c A LaTex expression showing bsquare root of 12bc
d A LaTex expression showing 1 over 3bsquare root of 14b{c to the power of 3 }
e A LaTex expression showing 1 over square root of 11{b to the power of 3c }
3
Convert the fractional exponent to a radical
A LaTex expression showing 2 to the power of -1 over 2 times {y} to the power of -5 over 2 times {z} to the power of -5 over 2
a A LaTex expression showing 1 over 4y{z to the power of 3 square root of {y to the power of 3 {z} to the power of 2 }}
b A LaTex expression showing 1 over {y to the power of 2 {z} to the power of 4 square root of 2yz}
c A LaTex expression showing 4{y} to the power of 4 {z} to the power of 2 square root of 5{y to the power of 3 z}
d A LaTex expression showing 1 over square root of 2{y to the power of 5{z to the power of 5 }}
e A LaTex expression showing 1 over y{z to the power of 2 square root of y{z to the power of 3 }}
4
Convert the fractional exponent to a radical
A LaTex expression showing 3 to the power of -1 over 2 times {b} to the power of -5 over 2 times {m} to the power of -3 over 2
a A LaTex expression showing {b} to the power of 3 {m} to the power of 2 square root of 3b{m to the power of 3 }
b A LaTex expression showing 1 over {b to the power of 4 msquare root of 2bm}
c A LaTex expression showing 1 over square root of 3{b to the power of 5{m to the power of 3 }}
d A LaTex expression showing 1 over b{m to the power of 2 square root of 5{b to the power of 3 m}}
e A LaTex expression showing 1 over {b to the power of 3 msquare root of bm}
5
Convert the fractional exponent to a radical
A LaTex expression showing 5 to the power of -1 over 2 times {b} to the power of -3 over 2 times {x} to the power of -5 over 2
a A LaTex expression showing 1 over square root of 5{b to the power of 3{x to the power of 5 }}
b A LaTex expression showing 1 over 2b{x to the power of 2 square root of 3bx}
c A LaTex expression showing 1 over bxsquare root of 6{b to the power of 3x }
d A LaTex expression showing 1 over 2{b to the power of 2 xsquare root of 5b{x to the power of 2 }}
e A LaTex expression showing 2{b} to the power of 3 xsquare root of 6bx
6
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 -1 over 2 times {y} to the power of -3 over 2
a A LaTex expression showing 1 over ysquare root of 3cy
b A LaTex expression showing 1 over {y to the power of 3 square root of 3{c to the power of 2 {y} to the power of 2 }}
c A LaTex expression showing 1 over 3ysquare root of 6c{y to the power of 3 }
d A LaTex expression showing 1 over square root of 3c{y to the power of 3 }
e A LaTex expression showing {y} to the power of 2 square root of 3{c to the power of 2 y}
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 2{p to the power of 2 {y} to the power of 2 square root of {p to the power of 2 y}}
b 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 }}
c A LaTex expression showing 1 over square root of 2{p to the power of 5{y to the power of 3 }}
d A LaTex expression showing 1 over pysquare root of 5p{y to the power of 3 }
e A LaTex expression showing {p} to the power of 3 ysquare root of {p to the power of 3 y}