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 $$\displaystyle (2x^3$y^2)(-5x^2$y^4$$)$ 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 $$\displaystyle \frac{a^7$b^{-2}$$}{$$a^3b^4$}$$, 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: $$\displaystyle \frac{(2x^4$y^{-2})^3$}{4x^5$y^{-1}$$}$

Accepted Answer

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^0$y^5)^3$?

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

Accepted Answer

Question 18

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

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

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