Question 1

A scientist measures the mass of a virus particle as $0.00000000045$ grams. What is this number in scientific notation?

Accepted Answer

$4.5 	imes 10^{-10}$

Question 2

Simplify the expression $\displaystyle (2x^3y^2)(-5x^2y^4)$ using the product rule for exponents.

Accepted Answer

$-10x^5y^6$

Question 3

Which of the following correctly applies the zero exponent rule to $(-7x^4y^0)^0$?

Accepted Answer

$1$

Question 4

A medication is prescribed in doses of $3.2 	imes 10^{-4}$ grams. What is this amount in standard notation?

Accepted Answer

$0.00032$ grams

Question 5

Simplify the following expression and write your answer with positive exponents: $\displaystyle \frac{5x^{-3}y^2}{10x^2y^{-4}}$

Accepted Answer

$\frac{y^6}{2x^5}$

Question 6

Which of the following is equivalent to $\displaystyle \frac{a^7b^{-2}}{a^3b^4}$, written with only positive exponents?

Accepted Answer

$\frac{a^4}{b^6}$

Question 7

A biologist records a cell population as $6.2 	imes 10^5$. How many cells is this in standard notation?

Accepted Answer

$620,000$

Question 8

Simplify the expression $\displaystyle (3x^{-2}y^3)^2$ and write your answer with positive exponents.

Accepted Answer

$\frac{9y^6}{x^4}$

Question 9

Which of the following is the correct application of the quotient rule for exponents to $\displaystyle \frac{z^{12}}{z^5}$?

Accepted Answer

$z^7$

Question 10

A chemist needs to dilute a solution to $2.5 	imes 10^{-3}$ liters. How many liters is this in standard notation?

Accepted Answer

$0.0025$ liters

Question 11

Simplify the following expression: $\displaystyle \frac{(2x^4y^{-2})^3}{4x^5y^{-1}}$

Question 12

Which of the following is equivalent to $\displaystyle (\frac{1}{3}x^{-2}y^4)^{-2}$, written with positive exponents?

Accepted Answer

$9x^4y^8$

Question 13

A city’s population is $3.45 	imes 10^6$. What is this number in standard notation?

Accepted Answer

$3,450,000$

Question 14

Simplify the following expression and write your answer with positive exponents: $\displaystyle \frac{4x^{-2}y^3}{8x^4y^{-1}}$

Accepted Answer

$\frac{y^4}{2x^6}$

Question 15

Which of the following is the correct simplification of $\displaystyle (x^0y^5)^3$?

Accepted Answer

$y^{15}$

Question 16

A computer can process $2.4 	imes 10^9$ instructions per second. How many instructions is this in standard notation?

Accepted Answer

$2,400,000,000$

Question 17

Simplify the following expression: $\displaystyle \frac{(x^2y^{-3})^2}{x^{-1}y^4}$

Question 18

Which of the following is the correct simplification of $\displaystyle (2x^0y^{-2})^3$?

Accepted Answer

$8y^{-6}$

Question 19

A virus sample contains $7.8 	imes 10^{-7}$ grams of material. What is this in standard notation?

Accepted Answer

$0.00000078$ grams

Exponents and Scientific Notation: College Algebra Study Notes

Study Guide - Practice Questions