Simplify: $$\frac{6x^8}{2x^3}$$

$$\frac{6}{2} \times x^{8-3} = 3x^5$$ .

Any non-zero number raised to the power of zero is 1: $$a^0 = 1$$ .

What is $$\frac{a^m}{a^m}$$ ?

Any non-zero number raised to the same power is 1: $$\frac{a^m}{a^m} = 1$$ .

Simplify: $$(x^2y^3)^2$$

$$x^{2 \times 2}y^{3 \times 2} = x^4y^6$$ .

Product, Quotient, & Power to a Power Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Product Rule for exponents?

Back

When multiplying two powers with the same base, add the exponents: $a^m \times a^n = a^{m+n}$ .

2.

FLASHCARD QUESTION

Front

What is the Quotient Rule for exponents?

Back

When dividing two powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$ .

3.

FLASHCARD QUESTION

Front

What is the Power of a Power Rule?

Back

When raising a power to another power, multiply the exponents: $(a^m)^n = a^{m \times n}$ .

4.

FLASHCARD QUESTION

Front

Simplify: $x^5 \times x^3$

Back

$x^{5+3} = x^8$ .

5.

FLASHCARD QUESTION

Front

Simplify: $\frac{x^7}{x^2}$

Back

$x^{7-2} = x^5$ .

6.

FLASHCARD QUESTION

Front

Simplify: $(2^3)^2$

Back

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

7.

FLASHCARD QUESTION

Front

What is $3^4 \times 3^2$ ?

Back

$3^{4+2} = 3^6 = 729$ .

8.

FLASHCARD QUESTION

Front

What is $\frac{5^9}{5^4}$ ?

Back

$5^{9-4} = 5^5 = 3125$ .

9.

FLASHCARD QUESTION

Front

Find the missing exponent: $2^{10} = 2^5 \times 2^?$

Back

@@2^{10} = 2^{5+5} ightarrow ? = 5@@.

10.

FLASHCARD QUESTION

Front

Simplify: $4m^3 \times 2m^2$

Back

$8m^{3+2} = 8m^5$ .

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