Exercise 16 Page 339

Let's take a look at the given questions.

In each of them we will need to use powers. To see which one is different let's analyze each question one at a time. Let's start with the first question.

First Question

First we can write the product in the denominator as a power.

1/3*3*3

ProdToPowThreeFac

a* a* a=a^3

1/3^3

Next we will use the definition of a negative exponent.

1/3^3

FracToNegExponent

1/a^m=a^(- m)

3^(-3)

The answer to this question is 3^(-3).

Second Question

We want to write 3 to the negative third. This means that we have a power with base 3 and exponent of - 3. 3^(- 3)

Third Question

This time we want to write 13 cubed as a power with an integer base. First let's raise 13 to the power of 3.

(1/3)^3

PowQuot

(a/b)^m=a^m/b^m

1^3/3^3

BaseOne

1^a=1

1/3^3

Next, let's use the definition of a negative exponent.

1/3^3

FracToNegExponent

1/a^m=a^(- m)

3^(-3)

The answer to this question is 3^(-3).

Fourth Question

Finally, we want to write (-3)*(-3)*(-3) as a power with an integer base. We can do this using the definition of a power.

(-3)*(-3)*(-3)

ProdToPowThreeFac

a* a* a=a^3

(-3)^3

The answer to this question is (-3)^3.

Conclusion

Let's compare the answers to all questions.

Question	Answer
Write 1333 using a negative exponent.	3^(-3)
Write 3 to the negative third.	3^(-3)
Write 13 cubed as a power with an integer base.	3^(-3)
Write (-3)(-3)(-3) as a power with an integer base.	( -3)^3

We can see that the last question is different because it has a different answer.

Hints

Check the answer

Practice exercises

Asses your skill

First Question

Second Question

Third Question

Fourth Question

Conclusion