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

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

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

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

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

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

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

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

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

Flashcard

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.A.1, HSA.APR.A.1

Standards-aligned

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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

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

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

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

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