What is the area of a rectangle with sides $$5x^2y^3$$ and $$4xy^2$$ ?

$$20x^{3}y^{5}$$ (Area = length × width) using exponent rules.

What is $$x^{-n}$$ equal to?

$$\frac{1}{x^n}$$ (Negative exponent rule).

What is the value of $$x^2 \times x^{-3}$$ ?

$$\frac{1}{x}$$ (Add the exponents: 2 + (-3) = -1).

What is the value of $$(3x^2y)^2$$ ?

$$9x^4y^2$$ (Apply the power of a product rule).

What is the value of $$\frac{(x^2y^3)^2}{xy}$$ ?

$$x^{3}y^{5}$$ (Apply the power of a power rule and quotient rule).

Exponent Product And Power Rules

Exponent Product and Power Rules

Flashcard

•

Mathematics

•

8th - 9th Grade

•

Practice Problem

•

Hard

•

CCSS

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

Standards-aligned

Wayground Content

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Student preview

15 questions

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FLASHCARD QUESTION

Front

What is the product of $x^a$ and $x^b$ ?

Back

$x^{a+b}$

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the power of a product rule?

Back

If $a$ and $b$ are numbers, then $(ab)^n = a^n b^n$ .

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the power of a power rule?

Back

If $a$ is a number and $m$ and $n$ are exponents, then $(a^m)^n = a^{mn}$ .

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the area of a rectangle with sides $7x^3y^8z^4$ and $10x^2y^8z^3$ ?

Back

$70x^{5}y^{16}z^{7}$ (Area = length × width) using exponent rules.

Tags

CCSS.HSA.APR.A.1

FLASHCARD QUESTION

Front

What is $x^0$ equal to?

Back

1 (Any non-zero number raised to the power of 0 is 1).

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the quotient rule for exponents?

Back

If $a$ is a number and $m$ and $n$ are exponents, then $\frac{a^m}{a^n} = a^{m-n}$ .

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the value of $x^3 \times x^2$ ?

Back

$x^{5}$ (Add the exponents).

Tags

CCSS.8.EE.A.1

FLASHCARD QUESTION

Front

What is the value of $\frac{x^5}{x^2}$ ?

Back

$x^{3}$ (Subtract the exponents).

Tags

CCSS.HSA.APR.A.1

FLASHCARD QUESTION

Front

What does $(xy)^3$ equal?

Back

$x^3y^3$ (Apply the power of a product rule).

Tags

CCSS.8.EE.A.1

10.

FLASHCARD QUESTION

Front

What is the value of $(2x^2)^3$ ?

Back

$8x^6$ (Apply the power of a power rule).

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