Discovery of Power to a Power

Discovery of Power to a Power

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Investigate: Powers to Powers

Use what you learned in the previous lessons to find a shortcut for simplifying expressions with powers.

What is the value of n?

(3⁶)²=3⁶ x 3⁶= 3ⁿ

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(5⁴)³=5⁴ x 5⁴ x 5⁴= 5ⁿ

What is the value of n?

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(2⁷)⁴=2⁷ x 2⁷ x 2⁷ x 2⁷=2ⁿ

^{What is the value of n?}

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(a³)²=a³ x a³= a^?

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Did you see the pattern?

(x⁵)⁸ = x^?

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In the previous example (x⁵)⁸, explain what you did to get your answer for x^?.

Multiple Choice

Complete the statement.

When simplifying (x⁵)⁸, just _______ the exponents to get x⁴⁰

• add

• subtract

• multiply

• divide

Open Ended

Raising a Power to a Power Property

(a^m)ⁿ=a^mn

Describe the raising a power to a power property in your own words.

Open Ended

With understanding the Raising a power to a power, what would this expression simplify to?

(2x³)⁴

Poll

What is your favorite pizza topping?

• plain

• pepperoni

• sausage

• mushroom

• ham and pineapples