What is the Product of Powers Property for numbers?

When multiplying numbers with the same base, add the exponents.

What is the simplified form of $$x^0$$ ?

$$x^0 = 1$$ for any non-zero x.

What is the result of multiplying a power by itself?

You add the exponents: $$a^m \times a^m = a^{m+m} = a^{2m}$$ .

Product of Powers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Product of Powers Property?

Back

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

2.

FLASHCARD QUESTION

Front

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

Back

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

3.

FLASHCARD QUESTION

Front

Simplify: $x^4 \times x^2$

Back

$x^{4+2} = x^6$ .

4.

FLASHCARD QUESTION

Front

What happens when you multiply powers with different bases?

Back

You cannot combine them using the Product of Powers Property; you must multiply the coefficients separately.

5.

FLASHCARD QUESTION

Front

Simplify: $10^5 \times 10^7$

Back

$10^{5+7} = 10^{12}$ .

6.

FLASHCARD QUESTION

Front

What is the rule for multiplying coefficients?

Back

Multiply the coefficients together and keep the variable part separate.

7.

FLASHCARD QUESTION

Front

Rewrite using a positive exponent: $g^{-7}$

Back

$\frac{1}{g^7}$ .

8.

FLASHCARD QUESTION

Front

Simplify: $(2m^4)(5m^2)$

Back

$2 \times 5 \times m^{4+2} = 10m^6$ .

9.

FLASHCARD QUESTION

Front

What is the result of $c^5 \times c^3 \times c^3$ ?

Back

$c^{5+3+3} = c^{11}$ .

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