Question 1

Which of the following is the correct simplification of $$\displaystyle \frac{a^5$ b^6$}{a^6$ b^5$}$$?

Accepted Answer

$$\displaystyle \frac{b}{a}$$

Question 2

Write $$0.00000059 in $$scientific notation.

Accepted Answer

$$5.9 	imes 10$$^{-7}$$

Question 3

Simplify the expression $$\displaystyle (x^3$ y^2$)^4$.

Accepted Answer

$$x^{12}$$ $$y^8$$

Question 4

A chemist has $$3.402 	imes 10^8$ molecules of a substance. How many molecules is this in standard form?

Accepted Answer

$$340,200,000$$

Question 5

Simplify the following expression: $$\displaystyle \frac{x^6$ y$$^{-3}$$}{x^2$ y^4$}.$$

Accepted Answer

$$x^4$$ $$y^{-7}$$

Question 6

Which of the following is equivalent to $$\displaystyle (2x^3$ y^2$)^2$?

Accepted Answer

$$4x^6$$ $$y^4$$

Question 7

A biologist records a bacteria population as $$6.77 	imes 10$$^{-3}$$ grams. What is this in standard form?

Accepted Answer

$$0.00677$$

Question 8

Simplify the expression $$\displaystyle \frac{(x^2$ y^3$)^2$$}{$$x^3 y$$}$.

Accepted Answer

$$x y^5$

Question 9

Which of the following is the result of $$\displaystyle (3x^2$ - 2x + 1)(x - 4)$$?

Accepted Answer

Question 10

A medical researcher dilutes a solution by a factor of $$\displaystyle \frac{1}{10^4$}. $$Express this as a decimal.

Accepted Answer

$$0.0001$$

Question 11

Simplify $$\displaystyle (4x^2$ y - 2y)^2$.

Accepted Answer

$$16x^4$$ $$y^2$$ - $$16x^2$$ $$y^2$$ + $$4y^2$$

Question 12

Divide: $$\displaystyle \frac{25b^7$ - 10b^5$ + 15b^2$}{5b^2$}.$$

Accepted Answer

$$5b^5$$ - $$2b^3 + 3$

Question 13

Simplify $$\displaystyle (x^2$ - 3x + 2)(x - 5)$$ using the distributive property.

Accepted Answer

Question 14

A physics experiment measures a distance as $$8.8 	imes 10^6$ meters. What is this in standard form?

Accepted Answer

$$8,800,000$$

Question 15

Simplify $$\displaystyle \frac{(x^4$ y^2$)^3$$}{$$x^5$$ $$y^4$$}$.

Accepted Answer

$$x^7$$ $$y^2$$

Question 16

Which of the following is the result of $$\displaystyle (2x^2$ - 3x + 4)(x + 5)$$?

Accepted Answer

Question 17

Simplify $$\displaystyle \frac{(3x^2$ y^3$)^2$$}{$$9x^3 y$$}$.

Accepted Answer

$$x y^5$

Question 18

A laboratory sample has a mass of $$1.2 	imes 10$$^{-5}$$ grams. Which of the following is the correct standard form?

Accepted Answer

$$0.000012$$

Question 19

Simplify $$\displaystyle (x^2$ - 2x + 1)(x^2$ + 2x + 1).$$

Accepted Answer

$$x^4$$ - $$4x^2 + 1$

Question 20

Divide: $$\displaystyle \frac{12x^5$ - 30x^3$ + 18x^2$}{6x^2$}.$$

Accepted Answer

$$2x^3 - 5x + 3$

Algebraic Expressions, Scientific Notation, and Polynomial Operations Review

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