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

This math topic focuses on simplifying radical expressions, specifically handling division of radicals with different indices and powers of the radicands. The expressions involve operations such as the nth root of a number raised to a power, divided by another nth root of a different number also raised to a power. The problems are designed to challenge understanding of manipulating and simplifying radical over radical expressions, converting them into simplified fractional forms. The topic is a component of a larger unit dedicated to simplifying radicals. Each question offers multiple choice answers requiring students to select the correct simplified form of the given radical expressions.

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 Radical Worksheet

Mobius Math Academy logo
Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical
1
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 16 to the power of 3 }{3-th root of 64 to the power of 3 }
a A LaTex expression showing 7 over 59
b A LaTex expression showing 4 over 7
c A LaTex expression showing 1
d A LaTex expression showing 2
e A LaTex expression showing 11 over 28
2
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 4 to the power of 3 }{2-th root of 4 to the power of 4 }
a A LaTex expression showing 7 over 12
b A LaTex expression showing 7 over 16
c A LaTex expression showing 9 over 14
d A LaTex expression showing 1 over 4
e A LaTex expression showing 2 over 7
3
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 64 to the power of 2 }{3-th root of 36 to the power of 3 }
a A LaTex expression showing 67 over 41
b A LaTex expression showing 23 over 12
c A LaTex expression showing 25 over 6
d A LaTex expression showing 64 over 27
e A LaTex expression showing 16 over 9
4
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 32 to the power of 2 }{3-th root of 16 to the power of 3 }
a A LaTex expression showing 2
b A LaTex expression showing 45 over 29
c A LaTex expression showing 29 over 10
d A LaTex expression showing 62 over 23
e A LaTex expression showing 1 over 2
5
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 8 to the power of 2 }{2-th root of 27 to the power of 2 }
a A LaTex expression showing 3 over 19
b A LaTex expression showing 7 over 52
c A LaTex expression showing 4 over 27
d A LaTex expression showing 2 over 5
e A LaTex expression showing 1 over 28
6
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 8 to the power of 2 }{3-th root of 8 to the power of 2 }
a A LaTex expression showing 1 over 7
b A LaTex expression showing 7 over 5
c A LaTex expression showing 4 over 11
d A LaTex expression showing 2
e A LaTex expression showing 7 over 2
7
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 32 to the power of 2 }{3-th root of 64 to the power of 2 }
a A LaTex expression showing 2
b A LaTex expression showing 44 over 17
c A LaTex expression showing 18 over 29
d A LaTex expression showing 9 over 14
e A LaTex expression showing 1 over 11
8
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 25 to the power of 3 }{2-th root of 32 to the power of 2 }
a A LaTex expression showing 25 over 56
b A LaTex expression showing 25 over 32
c A LaTex expression showing 11 over 29
d A LaTex expression showing 12 over 11
e A LaTex expression showing 10 over 29