Division with Mixed Index and Power of Radicand (Fraction) - Radical over Integer (Level 1)

This math topic focuses on simplifying radical expressions with varying roots and powers, which involve division by integers and results expressed as fractions. It includes specific techniques such as rationalizing denominators and handling mixed indices and powers of radicands like cube roots or square roots raised to a power, followed by division by an integer. The problems are structured to test and enhance understanding of simplifying complex radical expressions, which is a pivotal skill in advanced algebra topics.

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Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Radical over Integer Worksheet

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Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Radical over Integer
1
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 64 to the power of 2 }{16}
a A LaTex expression showing 1
b A LaTex expression showing 1 over 8
c A LaTex expression showing 24 over 13
d A LaTex expression showing 4 over 7
e A LaTex expression showing 25 over 33
2
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 9 to the power of 3 }{32}
a A LaTex expression showing 27 over 32
b A LaTex expression showing 1 over 2
c A LaTex expression showing 10 over 21
d A LaTex expression showing 3 over 5
e A LaTex expression showing 48 over 7
3
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 36 to the power of 3 }{81}
a A LaTex expression showing 8 over 3
b A LaTex expression showing 26 over 55
c A LaTex expression showing 81 over 73
d A LaTex expression showing 44 over 31
e A LaTex expression showing 262 over 65
4
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 8 to the power of 2 }{32}
a A LaTex expression showing 2 over 15
b A LaTex expression showing 5 over 52
c A LaTex expression showing 2 over 39
d A LaTex expression showing 1 over 8
e A LaTex expression showing 2 over 23
5
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 125 to the power of 2 }{64}
a A LaTex expression showing 2 over 11
b A LaTex expression showing 3 over 121
c A LaTex expression showing 25 over 64
d A LaTex expression showing 2 over 3
e A LaTex expression showing 37 over 43
6
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 4 to the power of 4 }{64}
a A LaTex expression showing 14 over 115
b A LaTex expression showing 7 over 24
c A LaTex expression showing 1 over 4
d A LaTex expression showing 2 over 39
e A LaTex expression showing 21 over 131
7
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 9 to the power of 3 }{16}
a A LaTex expression showing 9 over 8
b A LaTex expression showing 12 over 23
c A LaTex expression showing 1
d A LaTex expression showing 27 over 16
e A LaTex expression showing 7
8
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 8 to the power of 2 }{49}
a A LaTex expression showing 14 over 53
b A LaTex expression showing 1 over 13
c A LaTex expression showing 8 over 49
d A LaTex expression showing 4 over 93
e A LaTex expression showing 1 over 4