Division with Mixed Index and Power of Radicand (Fraction) - Radical over Integer (Level 2)

This math topic involves simplifying radical expressions where radicands (the numbers under the radical sign) are raised to a power and then divided by an integer. Specifically, it focuses on problems that deal with radicals having mixed indices. The expressions include radicals divided by integers, further requiring simplification to express answers in fractional form. This is part of a broader theme focusing on the simplification of radicals. Each problem presents a radical expression and multiple-choice answers, aiming to hone skills in simplifying and manipulating complex radical forms.

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

more
View

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

Mobius Math Academy logo
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 216 to the power of 2 }{27}
a A LaTex expression showing 23 over 9
b A LaTex expression showing 44 over 21
c A LaTex expression showing 4 over 3
d A LaTex expression showing 15 over 37
e A LaTex expression showing 18 over 13
2
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 9 to the power of 3 }{81}
a A LaTex expression showing 1 over 6
b A LaTex expression showing 47 over 149
c A LaTex expression showing 1 over 3
d A LaTex expression showing 7 over 114
e A LaTex expression showing 15 over 101
3
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 64 to the power of 2 }{32}
a A LaTex expression showing 14 over 5
b A LaTex expression showing 25 over 22
c A LaTex expression showing 35 over 31
d A LaTex expression showing 100 over 39
e A LaTex expression showing 2
4
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 8 to the power of 4 }{64}
a A LaTex expression showing 5 over 43
b A LaTex expression showing 23 over 66
c A LaTex expression showing 29 over 26
d A LaTex expression showing 1 over 4
e A LaTex expression showing 19 over 78
5
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 216 to the power of 2 }{8}
a A LaTex expression showing 5 over 4
b A LaTex expression showing 58 over 11
c A LaTex expression showing 31 over 8
d A LaTex expression showing 7 over 2
e A LaTex expression showing 9 over 2
6
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 9 to the power of 3 }{64}
a A LaTex expression showing 1 over 18
b A LaTex expression showing 9 over 64
c A LaTex expression showing 14 over 5
d A LaTex expression showing 19 over 100
e A LaTex expression showing 1 over 32
7
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 16 to the power of 3 }{8}
a A LaTex expression showing 2
b A LaTex expression showing 1
c A LaTex expression showing 7 over 5
d A LaTex expression showing 25 over 16
e A LaTex expression showing 5 over 3
8
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 36 to the power of 3 }{16}
a A LaTex expression showing 273 over 5
b A LaTex expression showing 27 over 2
c A LaTex expression showing 67 over 6
d A LaTex expression showing 358 over 35
e A LaTex expression showing 199 over 26