Power of Quotients and Exponents

The video tutorial explains the power of a power rule, which involves multiplying exponents when raising an exponential expression to another power. It provides examples such as raising 2^2 to the 3rd power, resulting in 2^6. The tutorial also covers the power of a quotient property, which states that raising a rational expression to an exponent is equivalent to raising both the numerator and denominator to that exponent. Examples include raising (4/2)^2 to get (4^2)/(2^2).

What does the power of a power rule state?

• Add the exponents together.

• Subtract the exponents.

• Divide the exponents.

• Multiply the exponents together.

If you have 3^2 raised to the 4th power, what is the result?

• 3^12

• 3^16

• 3^8

• 3^6

How do you express (x^3)^5 using the power of a power rule?

• x^8

• x^15

• x^5

• x^3

What is the power of a quotient property?

• Do not raise any part to the power.

• Raise only the denominator to the power.

• Raise both the numerator and denominator to the power.

• Raise only the numerator to the power.

How would you simplify (5/2)^3 using the power of a quotient property?

• 5^3 / 2^3

• 5^2 / 2^2

• 5 / 2^3

• 5^3 / 2

What is the result of (7/3)^2?

• 7 / 3^2

• 7^2 / 3^2

• 7^2 / 3

• 7^3 / 3^3

If (a/b)^4 is simplified using the power of a quotient property, what is the result?

• a^4 / b

• a / b^4

• a^4 / b^4

• a^2 / b^2

How do you express (2/5)^3 using the power of a quotient property?

• 2^2 / 5^2

• 2^3 / 5^3

• 2 / 5^3

• 2^3 / 5