Examples with solutions for Square Root Quotient Property: Same base and different indicator

Exercise #1

Solve the following exercise:

3653610= \frac{\sqrt[5]{36}}{\sqrt[10]{36}}=

Video Solution

Answer

36110 36^{\frac{1}{10}}

Exercise #2

Solve the following exercise:

4346= \frac{\sqrt[3]{4}}{\sqrt[6]{4}}=

Video Solution

Answer

416 4^{\frac{1}{6}}

Exercise #3

Solve the following exercise:

536533= \frac{\sqrt[6]{5^3}}{\sqrt[3]{5^3}}=

Video Solution

Answer

5 \sqrt{5}

Exercise #4

Solve the following exercise:

554= \frac{\sqrt{5}}{\sqrt[4]{5}}=

Video Solution

Answer

54 \sqrt[4]{5}

Exercise #5

Solve the following exercise:

3436= \frac{\sqrt[4]{3}}{\sqrt[6]{3}}=

Video Solution

Answer

3112 3^{\frac{1}{12}}

Exercise #6

Solve the following exercise:

4243= \frac{\sqrt[2]{4}}{\sqrt[3]{4}}=

Video Solution

Answer

416 4^{\frac{1}{6}}

Exercise #7

Solve the following exercise:

6362= \frac{\sqrt[3]{6}}{\sqrt[2]{6}}=

Video Solution

Answer

66 \sqrt[6]{6}

Exercise #8

Solve the following exercise:

5354= \frac{\sqrt[3]{5}}{\sqrt[4]{5}}=

Video Solution

Answer

Answers (a) and (c)

Exercise #9

Solve the following exercise:

623624= \frac{\sqrt[3]{6^2}}{\sqrt[4]{6^2}}=

Video Solution

Answer

616 6^\frac{1}{6}

Exercise #10

Solve the following exercise:

2425= \frac{\sqrt[4]{2}}{\sqrt[5]{2}}=

Video Solution

Answer

2120 2^{\frac{1}{20}}