Understanding the Power of Powers Rule

The video tutorial explores the power of power's rule in mathematics, demonstrating how to simplify expressions with exponents. It begins with an example involving the distribution of an exponent across a product of powers, leading to a simplified result. The tutorial then transitions to simplifying expressions with rational exponents, converting them into rational form and distributing exponents to achieve a simplified expression. Finally, the video addresses fractional exponents, showing how to simplify them by distributing and canceling terms. Throughout, the tutorial emphasizes the step-by-step process of simplification, providing clear examples and calculations.

What is the initial expression given in the video for the power of powers rule?

• 4 to the one half times 4 to the one fifth all to the tenth

• 4 to the one third times 4 to the one fourth all to the sixth

• 5 to the three halves all to the two thirds

• 4 to the one fourth times 4 to the one third all to the fifth

How is the exponent 6 distributed in the expression 4^(1/3) * 4^(1/4) all to the 6th?

• It is subtracted from each exponent

• It is added to each exponent

• It is divided by each exponent

• It is multiplied with each exponent

What is the simplified result of 4^(1/3 * 6) * 4^(1/4 * 6)?

• 4^2 * 4^3

• 4^3 * 4^(1/2)

• 4^2 * 4^(3/2)

• 4^(1/2) * 4^3

What is the final simplified answer for the first problem?

• 128

• 64

• 256

• 32

How are the expressions rewritten in the second problem?

• As rational exponents

• As decimal numbers

• As improper fractions

• As whole numbers

What is the result of distributing 10 to the exponents in the second problem?

• 4^5 * 4^2

• 4^2 * 4^5

• 4^3 * 4^4

• 4^4 * 4^3

What is the final expression for the second problem?

• 4^6

• 4^7

• 4^9

• 4^8

In the third problem, what operation is performed on the exponents 3/2 and 2/3?

• Addition

• Division

• Subtraction

• Multiplication

What is the simplified exponent for 5^(3/2 * 2/3)?

• 5^(1/3)

• 5^(3/4)

• 5^(1/2)

• 5^(2/3)

What is the final simplified expression for the third problem?

• 5^(1/3)

• 5^(2/3)

• 5^(1/2)

• 5^(3/4)