Define exponentiation in the context of the power to power rule.

Exponentiation is the process of raising a number (the base) to a power (the exponent).

What is the general formula for the power to power rule?

If $$a$$ is a base and $$m, n$$ are exponents, then $$(a^m)^n = a^{m \times n}$$ .

What is the simplified form of $$\text{If } (2x^2y^3)^3?$$

$$2^3 \times (x^2)^3 \times (y^3)^3 = 8x^6y^9$$ .

What is the significance of the power to power rule in algebra?

It simplifies expressions involving exponents, making calculations easier.

Provide an example of a real-world application of the power to power rule.

In scientific notation, when multiplying powers of ten, the power to power rule helps simplify calculations.

Power to power rule Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the power to power rule in exponents?

Back

When raising a power to another power, you multiply the exponents.

Tags

CCSS.8.EE.A.1

2.

FLASHCARD QUESTION

Front

Simplify: $\text{If } a^m \text{ is raised to the power of } n, \text{ what is the result?}$

Back

$a^{m \times n}$ .

Tags

CCSS.8.EE.A.1

3.

FLASHCARD QUESTION

Front

Simplify: $\text{What is } (x^2)^3?$

Back

$x^{2 \times 3} = x^6$ .

Tags

CCSS.HSA.APR.A.1

4.

FLASHCARD QUESTION

Front

Simplify: $\text{What is } (2^3)^2?$

Back

$2^{3 \times 2} = 2^6 = 64$ .

Tags

CCSS.8.EE.A.1

5.

FLASHCARD QUESTION

Front

What happens to the base when applying the power to power rule?

Back

The base remains the same; only the exponents are multiplied.

Tags

CCSS.8.EE.A.1

6.

FLASHCARD QUESTION

Front

Simplify: $\text{What is } (m^3)^5?$

Back

$m^{3 \times 5} = m^{15}$ .

Tags

CCSS.8.EE.A.1

7.

FLASHCARD QUESTION

Front

Simplify: $\text{What is } (3y^4)^2?$

Back

$3^2 \times (y^4)^2 = 9y^{4 \times 2} = 9y^8$ .

Tags

CCSS.HSA.APR.A.1

8.

FLASHCARD QUESTION

Front

Simplify: $\text{What is } (3x^3y^5)^4?$

Back

$3^4 \times (x^3)^4 \times (y^5)^4 = 81x^{12}y^{20}$ .

Tags

CCSS.HSA.APR.A.1

9.

FLASHCARD QUESTION

Front

What is the result of $\text{If } (4xy^3)^3?$

Back

$4^3 \times x^3 \times (y^3)^3 = 64x^3y^9$ .

Tags

CCSS.8.EE.A.1

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