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Radicals

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

This math topic practices skills related to simplifying radicals involving division of expressions with mixed indices and different powers of the radicand. The specific skill focused on is simplifying complex expressions where both the numerator and denominator are radicals, determining the integer value to which these expressions simplify. Each problem provides multiple choice answers, enhancing understanding and application of radical simplification rules.

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

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

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Radicals - Division with Mixed Index and Power of Radicand (Integer) - Radical over Radical
1
What integer does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 81 to the power of 3 }{2-th root of 81 to the power of 2 }
a
1
b
10
c
6
d
3
e
4
f
7
2
What integer does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 16 to the power of 2 }{3-th root of 16 to the power of 3 }
a
6
b
4
c
2
d
7
e
5
f
1
3
What integer does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 16 to the power of 3 }{2-th root of 16 to the power of 2 }
a
5
b
2
c
4
d
3
e
1
f
10
4
What integer does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 64 to the power of 2 }{2-th root of 4 to the power of 3 }
a
4
b
2
c
5
d
3
e
8
f
1
5
What integer 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 4 to the power of 3 }
a
11
b
15
c
16
d
8
e
2
f
4
6
What integer does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 64 to the power of 2 }{2-th root of 8 to the power of 2 }
a
3
b
1
c
2
d
4
e
6
f
11
7
What integer does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 36 to the power of 3 }{3-th root of 36 to the power of 3 }
a
7
b
6
c
10
d
1
e
3
f
8
8
What integer does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 4 to the power of 5 }{3-th root of 8 to the power of 4 }
a
8
b
7
c
11
d
1
e
2
f
3