Question 1

Simplify the expression. Write the result using positive exponents only. Assume that all bases are not equal to 0.

$$\frac{p^6$ p}{p$$^{-1}$$}$$

Accepted Answer

$$p^8$$

Question 2

If $$p$$ represents the population of a bacteria colony and the population triples every hour, which of the following expressions represents the population after 4 hours if the initial population is $$p_0$$?

Accepted Answer

$$p_0$$ \cdot $$3^4$$

Question 3

Which of the following is equivalent to $$\frac{p^3$}{p^7$}$$, written with positive exponents only?

Accepted Answer

$$\frac{1}{p^4$}$$

Question 4

A medication is administered such that the amount in the bloodstream halves every hour. If the initial dose is $$d$$, which expression gives the amount after 5 hours?

Accepted Answer

$$d \cdot \frac{1}{2^5$}$$

Question 5

Simplify the following expression and write your answer using positive exponents only: $$\left(\frac{p^2$}{p^5$}\$$right)^3$$

Accepted Answer

$$\frac{1}{p^9$}$$

Question 6

Which of the following is the correct simplification of $$p^0$$ \cdot $$p^4$$?

Accepted Answer

$$p^4$$

Question 7

If $$p is a $$nonzero number, which of the following is equivalent to $$\frac{p$$^{-3}$$}{p^2$}$$?

Accepted Answer

$$p^{-5}$$

Question 8

A scientist dilutes a solution so that its concentration is reduced by a factor of $$p^2$$ every hour. If the initial concentration is $$C_0$$, what is the concentration after 3 hours?

Accepted Answer

$$C_0$$ \cdot \frac{1}{$$p^6$$}$$

Question 9

Simplify the following expression and write your answer using positive exponents only: $$\frac{p^4$}{p$$^{-2}$$}$$

Accepted Answer

$$p^6$$

Question 10

Which of the following is the correct simplification of $$\$$left(p^{-2}$$\$$right)^{-3}$$?

Accepted Answer

$$p^6$$

Simplifying Expressions with Exponents

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