Question 1

Simplify the following expression and choose the correct answer:

$$
\left( \frac{1}{9} x$$^{-2}$$ y$$^{7}$$ \right) \left( \frac{1}{7} x$$^{2}$$ y$$^{-9}$$ \right)
$$
What is the simplified form?

Accepted Answer

$$\frac{1}{63} y$$^{-2}$$

Question 2

Which property of exponents is used to combine $$x^{-2}$$ and $$x^{2} in $$the expression:

$$
\left( \frac{1}{9} x$$^{-2}$$ y$$^{7}$$ \right) \left( \frac{1}{7} x$$^{2}$$ y$$^{-9}$$ \right)
$$?

Accepted Answer

Product of powers property: $$a^{m}$$ $$a^{n}$$ = $$a^{m+n}$$

Question 3

If $$y^{-2}$$ appears in your simplified answer, what is the equivalent expression using only positive exponents?

Accepted Answer

$$\frac{1}{y$$^{2}$$}$$

Question 4

What is the coefficient in the simplified form of the expression:

$$
\left( \frac{1}{9} x$$^{-2}$$ y$$^{7}$$ \right) \left( \frac{1}{7} x$$^{2}$$ y$$^{-9}$$ \right)
$$?

Accepted Answer

$$\frac{1}{63}$$

Question 5

Which of the following is the correct step to combine the $$y$$ terms in the expression:

$$y^{7}$$ $$y^{-9}$$?

Accepted Answer

$$y^{7 + (-9)}$$ = $$y^{-2}$$

Question 6

Which of the following best describes the process used to simplify the product of two exponential expressions with the same base?

Accepted Answer

Add the exponents if the bases are the same.

Question 7

Given the expression $$x^{-2}$$ $$x^{2}$$, what is the result?

Accepted Answer

$$x^{0}$$

Question 8

If you simplify $$x^{0}$$, what do you get (for $$x 
eq 0$$)?

Accepted Answer

$$1$$

Question 9

Which of the following is equivalent to the simplified answer of the original expression, written with only positive exponents?

Accepted Answer

$$\frac{1}{63 y$$^{2}$$}$$

Question 10

If you multiply $$\frac{1}{9}$$ and $$\frac{1}{7}$$, what is the result?

Accepted Answer

$$\frac{1}{63}$$

Multiplying Expressions with Exponents and Negative Powers

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