Convert Square Root, Values and Variables, to Exponents - Positive (Level 2)

This math topic focuses on converting radicals into fractional exponents. Learners are presented with problems involving both numerical values and variables under square roots, which they must rewrite using fractional exponents. This skill is an integral part of simplifying radicals, and the problems escalate in difficulty through multiple questions and possible answers. The exercise strengthens understanding of how exponents and radicals are interrelated, aiding in algebraic manipulation and simplification tasks. Multiple choice answers associated with each problem allow for testing comprehension and mistakes in conversion.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Radicals - Convert Square Root, Values and Variables, to Exponents - Positive Worksheet

Mobius Math Academy logo
Radicals - Convert Square Root, Values and Variables, to Exponents - Positive
1
Convert the radical to a fractional exponent
A LaTex expression showing square root of 5{y to the power of 3 {c} to the power of 5 }
a A LaTex expression showing 10 to the power of 1 over 2 times {y} to the power of 3 over 2 times {c} to the power of 5 over 2
b A LaTex expression showing 5 to the power of 1 over 3 times {y} to the power of 3 over 3 times {c} to the power of 5 over 3
c A LaTex expression showing 5 to the power of 1 over 2 times {y} to the power of 3 over 2 times {c} to the power of 5 over 2
d A LaTex expression showing 5 to the power of 1 over 2 times {y} to the power of 2 over 2 times {c} to the power of 7 over 2
2
Convert the radical to a fractional exponent
A LaTex expression showing square root of 5{c to the power of 3 {b} to the power of 3 }
a A LaTex expression showing 5 to the power of 1 over 2 times {c} to the power of 3 over 2 times {b} to the power of 3 over 2
b A LaTex expression showing 15 to the power of 1 over 2 times {c} to the power of 3 over 2 times {b} to the power of 3 over 2
c A LaTex expression showing 20 to the power of 1 over 2 times {c} to the power of 3 over 2 times {b} to the power of 3 over 2
d A LaTex expression showing 5 to the power of 1 over 2 times {c} to the power of 2 over 2 times {b} to the power of 4 over 2
e A LaTex expression showing 10 to the power of 1 over 2 times {c} to the power of 3 over 2 times {b} to the power of 3 over 2
3
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{z to the power of 3 y}
a A LaTex expression showing 2 to the power of 1 over 3 times {z} to the power of 3 over 3 times y to the power of 1 over 3
b A LaTex expression showing 4 to the power of 1 over 2 times {z} to the power of 3 over 2 times y to the power of 1 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {z} to the power of 3 over 2 times y to the power of 1 over 2
d A LaTex expression showing 2 to the power of -1 over 2 times {z} to the power of -3 over 2 times y to the power of -1 over 2
e A LaTex expression showing 2 to the power of 1 over 2 times {z} to the power of 2 over 2 times {y} to the power of 2 over 2
4
Convert the radical to a fractional exponent
A LaTex expression showing square root of 7{x to the power of 3 {z} to the power of 3 }
a A LaTex expression showing 7 to the power of 1 over 2 times {x} to the power of 4 over 2 times {z} to the power of 5 over 2
b A LaTex expression showing 7 to the power of -1 over 2 times {x} to the power of -3 over 2 times {z} to the power of -3 over 2
c A LaTex expression showing 14 to the power of 1 over 2 times {x} to the power of 3 over 2 times {z} to the power of 3 over 2
d A LaTex expression showing 7 to the power of 1 over 2 times {x} to the power of 3 over 2 times {z} to the power of 3 over 2
e A LaTex expression showing 21 to the power of 1 over 2 times {x} to the power of 3 over 2 times {z} to the power of 3 over 2
5
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2{x to the power of 3 {d} to the power of 5 }
a A LaTex expression showing 2 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
b A LaTex expression showing 8 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
c A LaTex expression showing 4 to the power of 1 over 2 times {x} to the power of 3 over 2 times {d} to the power of 5 over 2
d A LaTex expression showing 2 to the power of 1 over 3 times {x} to the power of 3 over 3 times {d} to the power of 5 over 3
e A LaTex expression showing 2 to the power of -1 over 2 times {x} to the power of -3 over 2 times {d} to the power of -5 over 2
6
Convert the radical to a fractional exponent
A LaTex expression showing square root of 2xy
a A LaTex expression showing 6 to the power of 1 over 2 times x to the power of 1 over 2 times y to the power of 1 over 2
b A LaTex expression showing 2 to the power of 1 over 2 times x to the power of 1 over 2 times y to the power of 1 over 2
c A LaTex expression showing 2 to the power of 1 over 2 times {x} to the power of 2 over 2 times
d A LaTex expression showing 4 to the power of 1 over 2 times x to the power of 1 over 2 times y to the power of 1 over 2
e A LaTex expression showing 2 to the power of 1 over 2 times {x} to the power of 2 over 2 times {y} to the power of 3 over 2
7
Convert the radical to a fractional exponent
A LaTex expression showing square root of 3{c to the power of 5 {m} to the power of 3 }
a A LaTex expression showing 3 to the power of -1 over 2 times {c} to the power of -5 over 2 times {m} to the power of -3 over 2
b A LaTex expression showing 3 to the power of 1 over 2 times {c} to the power of 5 over 2 times {m} to the power of 5 over 2
c A LaTex expression showing 3 to the power of 1 over 2 times {c} to the power of 5 over 2 times {m} to the power of 4 over 2
d A LaTex expression showing 9 to the power of 1 over 2 times {c} to the power of 5 over 2 times {m} to the power of 3 over 2
e A LaTex expression showing 3 to the power of 1 over 2 times {c} to the power of 5 over 2 times {m} to the power of 3 over 2
8
Convert the radical to a fractional exponent
A LaTex expression showing square root of 7b{y to the power of 5 }
a A LaTex expression showing 7 to the power of 1 over 2 times {y} to the power of 4 over 2
b A LaTex expression showing 7 to the power of -1 over 2 times b to the power of -1 over 2 times {y} to the power of -5 over 2
c A LaTex expression showing 7 to the power of 1 over 2 times b to the power of 1 over 2 times {y} to the power of 5 over 2
d A LaTex expression showing 7 to the power of 1 over 3 times b to the power of 1 over 3 times {y} to the power of 5 over 3
e A LaTex expression showing 7 to the power of 1 over 2 times {b} to the power of 2 over 2 times {y} to the power of 6 over 2