Power Rules and Fraction Exponents

The video tutorial explains the power rule for quotients, demonstrating how to apply it to various examples. It covers the rule that states if x and y are real numbers and m and n are positive integers, then (x/y)^m equals x^m/y^n. The tutorial provides five examples, each illustrating the application of the power rule to different expressions, including those with negative bases and variables.

What is the power rule for a quotient when x and y are real numbers and m and n are positive integers?

• The quantity of x divided by y raised to the power of m is equal to x to the power of n over y to the power of m.

• The quantity of x divided by y raised to the power of m is equal to x to the power of n times y to the power of m.

• The quantity of x divided by y raised to the power of m is equal to x to the power of m over y to the power of n.

• The quantity of x divided by y raised to the power of m is equal to x to the power of m times y to the power of n.

In Example 1, what is the result of raising the fraction a/b to the power of 8?

• a to the power of 8 over b to the power of 8

• a to the power of 8 times b to the power of 8

• a to the power of 4 over b to the power of 4

• a to the power of 4 times b to the power of 4

In Example 2, what is the simplified result of raising the fraction -3/5 to the power of 3?

• 27/125

• -27/125

• 27/25

• -27/25

In Example 3, what is the simplified result of raising the fraction 2g/h to the power of 5?

• 16g to the power of 5 times h to the power of 5

• 32g to the power of 5 times h to the power of 5

• 16g to the power of 5 over h to the power of 5

• 32g to the power of 5 over h to the power of 5

In Example 4, what is the simplified result of raising the fraction -7/8 to the power of 2?

• 49/64

• -49/64

• 49/32

• -49/32

In Example 5, what is the simplified result of raising the expression (x^3 * y) / z^4 to the power of 6?

• x to the power of 18 times y to the power of 4 over z to the power of 12

• x to the power of 18 times y to the power of 6 over z to the power of 12

• x to the power of 18 times y to the power of 4 over z to the power of 24

• x to the power of 18 times y to the power of 6 over z to the power of 24