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

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Lessons for Grade 8

Common Core For Grade 8

• 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:
(15^{3})^{9}

Exercise 2:
((-2)^{5})^{8}

Exercise 3:
(3.4^{17})^{4}

Exercise 4:

Let s be a number.
(s^{17})^{4}

Exercise 5:

Sarah wrote that (3^{5})^{7} = 3^{12}. 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 y^{24} - 256 = 0. What equation does the number x = y^{4} satisfy?

For any number x and any positive integers m and n,

(xy)^{n} = x^{n}y^{n}

Exercise 7:
(11 x 4)^{9}

Exercise 8:
(3^{2} x 7^{4})^{5}

Exercise 9:

Let a, b, and c be numbers.

(3^{2}a^{4})^{5}

Exercise 10

Let x be a number.

(5x)^{7}

Exercise 11

Let x and y be numbers.

(5xy^{2})^{7}

Exercise 12

Let a, b, and c be numbers.

(a^{2}bc^{3})^{4}