Evaluate $$\frac{4^{-2}}{4^{-5}}$$ .

$$4^{-2 - (-5)} = 4^{3} = 64$$ .

Simplify $$\frac{5^{-1}}{5^{-3}}$$ .

$$5^{-1 - (-3)} = 5^{2} = 25$$ .

Evaluate $$\frac{z^6}{z^{-2}}$$ .

$$z^{6 - (-2)} = z^{6 + 2} = z^8$$ .

What is the value of $$\frac{10^{-3}}{10^{-1}}$$ ?

$$10^{-3 - (-1)} = 10^{-2} = \frac{1}{100}$$ .

Negative exponents and Quotient Rule 11.7 ReDOL Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, $a^{-n} = \frac{1}{a^n}$ .

2.

FLASHCARD QUESTION

Front

What is the Quotient Rule for exponents?

Back

The Quotient Rule states that when dividing two powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$ .

3.

FLASHCARD QUESTION

Front

Evaluate $x^{-3}$ .

Back

$\frac{1}{x^3}$ .

4.

FLASHCARD QUESTION

Front

Simplify $\frac{a^5}{a^{-2}}$ .

Back

$a^{5 - (-2)} = a^{5 + 2} = a^7$ .

5.

FLASHCARD QUESTION

Front

What does $m^{-n}$ equal?

Back

$\frac{1}{m^n}$ .

6.

FLASHCARD QUESTION

Front

Simplify $\frac{2^5}{2^{-3}}$ .

Back

$2^{5 - (-3)} = 2^{5 + 3} = 2^8$ .

7.

FLASHCARD QUESTION

Front

Evaluate $\frac{b^4}{b^2}$ using the Quotient Rule.

Back

$b^{4-2} = b^2$ .

8.

FLASHCARD QUESTION

Front

What is $\frac{1}{x^{-4}}$ ?

Back

$x^4$ .

9.

FLASHCARD QUESTION

Front

Simplify $\frac{3x^{-2}}{x^{-5}}$ .

Back

$3x^{-2 - (-5)} = 3x^{3}$ .

10.

FLASHCARD QUESTION

Front

What is the result of $\frac{y^3}{y^5}$ ?

Back

$y^{3-5} = y^{-2} = \frac{1}{y^2}$ .

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