Numbers in Exponential Form Raised to a Power

Examples, videos, and solutions to help Grade 8 students learn how to take powers of powers.

New York State Common Core Math Grade 8, Module 1, 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,
(x^m)ⁿ = x^mn
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

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