 # Numbers in Exponential Form Raised to a Power

Videos and solutions to help Grade 8 students learn how to take powers of powers.

## New York State Common Core Math Module 1, Grade 8, Lesson 3

### Lesson 3 Student Outcomes

• Students will know how to take powers of powers. Students will know that when a product is raised to a power, each factor of the product is raised to that power.
• Students will write simplified, equivalent numeric and symbolic expressions using this new knowledge of powers.

Classwork

For any number x and any positive integers m and n,
(xm)n = xmn
Exercise 1: (153)9
Exercise 2: ((-2)5)8
Exercise 3: (3.417)4
Exercise 4:
Let s be a number. (s17)4
Exercise 5:
Sarah wrote that (35)7 = 312. Correct her mistake. Write an exponential expression using a base of 3 and exponents of 5, 7, and 12 that would make her answer correct.
Exercise 6:
A number y satisfies y24 - 256 = 0. What equation does the number x = y4 satisfy?
For any number x and any positive integers m and n,
(xy)n = xnyn
Exercise 7: (11 x 4)9
Exercise 8: (32 x 74)5
Exercise 9:
Let a, b, and c be numbers.
(32a4)5
Exercise 10
Let x be a number.
(5x)7
Exercise 11
Let x and y be numbers.
(5xy2)7
Exercise 12
Let a, b, and c be numbers.
(a2bc3)4 