What is the general rule for simplifying expressions with negative exponents?

Change the sign of the exponent and take the reciprocal of the base.

If $$b^{-n} = \frac{1}{b^n}$$ , what is $$3^{-2}$$ ?

$$\frac{1}{3^2} = \frac{1}{9}$$ .

What happens to a number when raised to the power of zero?

It equals 1, as long as the base is not zero.

Zero and Negative Exponents Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the value of $x^0$ for any non-zero number x?

Back

1

2.

FLASHCARD QUESTION

Front

What does a negative exponent indicate?

Back

A negative exponent indicates that the base should be taken as the reciprocal raised to the opposite positive exponent.

3.

FLASHCARD QUESTION

Front

What is the value of $a^{-n}$ ?

Back

$\frac{1}{a^n}$ for any non-zero number a and positive integer n.

4.

FLASHCARD QUESTION

Front

Simplify $6y^{-2}z^2$ .

Back

$\frac{6z^2}{y^2}$ .

5.

FLASHCARD QUESTION

Front

Simplify $5ay^{-3}$ .

Back

$\frac{5a}{y^3}$ .

6.

FLASHCARD QUESTION

Front

Simplify $5v^{-2}$ .

Back

$\frac{5}{v^2}$ .

7.

FLASHCARD QUESTION

Front

What is the value of $6^{-2}$ ?

Back

$\frac{1}{36}$ .

8.

FLASHCARD QUESTION

Front

What is the value of $4^{-1}$ ?

Back

$\frac{1}{4}$ .

9.

FLASHCARD QUESTION

Front

If $x^{-m} = \frac{1}{x^m}$ , what is $2^{-3}$ ?

Back

$\frac{1}{2^3} = \frac{1}{8}$ .

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