Question 1

Simplify the following expression using only positive exponents: 
$$
\frac{16z$$^{-9}$$}{4x^5$z^{-2}$$}
$

Accepted Answer

$$\frac{4}{x^5$z^7$$}$

Question 2

Express $$6.17 	imes 10^5$ in decimal form.

Accepted Answer

$$617000$$

Question 3

Convert $$0.000000475 to $$scientific notation.

Accepted Answer

$$4.75 	imes 10$$^{-7}$$

Question 4

Divide and write the result using scientific notation: 
$$
\frac{3.4 	imes 10^9$}{5.6 	imes 10$$^{-3}$$}
$$

Accepted Answer

$$6.07 	imes 10$$^{11}$$

Question 5

Evaluate the polynomial $$-5x^3$$ + $$8x^2 - 9x - 10$ for x = -3$.

Accepted Answer

$$-208$$

Question 6

Factor completely: $$32x^3y$$ - $$36xy^2$$ + $$16x^2y$

Accepted Answer

$$4xy(8x^2 - 9y + 4x$$)$$

Question 7

Which value of $$x$$ makes the rational expression $$\frac{7}{x-7} + \frac{4}{x+3} = \frac{10x}{x^2$ - 4x - 21}$$ undefined?

Accepted Answer

$$x = 7$$ and $$x = -3$$

Question 8

Simplify the following expression: 
$$
\frac{21x^2$ - 189}{49x^2$ - 441}
$$

Accepted Answer

$$\frac{3(x-3)}{7(x+3)}$$

Question 9

Perform the operation and simplify: $$(x+5)(x-3)$$

Accepted Answer

$$x^2 + 2x - 15$

Question 10

Which of the following is the correct simplification of $$(3xy^3)^2$(9x^8y^2$)$?

Accepted Answer

$$81x^{10}y^8$

Question 11

Factor completely: $$2x^3$$ + $$10x^2 + 7x + 35$

Accepted Answer

$$(x+5)(2x^2 + 7$$)$$

Question 12

Simplify the following rational expression: 
$$
\frac{a-b}{4b-4a}
$$

Accepted Answer

$$-\frac{1}{4}$$

Question 13

Solve for $$x in $$the equation: $$\frac{7}{x-7} + \frac{4}{x+3} = \frac{10x}{x^2$ - 4x - 21}$$, and state any restrictions.

Accepted Answer

$$x = 2$$, $$x 
eq 7, -3$$

Question 14

Which of the following is undefined for $$x = 3$$?

Accepted Answer

$$\frac{1}{x-3}$$

Question 15

Perform the operation and simplify: 
$$
\frac{x^2$ - x - 6}{x^2$ - 3x - 10}
$$

Accepted Answer

$$\frac{x+2}{x-5}$$

Question 16

A chemist mixes two solutions, one with a concentration of $$x$$ grams per liter and another with $$x+5$$ grams per liter. If the total mixture is represented by $$(x+5)(x-3)$$, what is the expanded form?

Accepted Answer

$$x^2 + 2x - 15$

Question 17

Simplify the following: 
$$
\left(\frac{4x^6$}{5y^2$}\$$right)^{-3}$$
$$

Accepted Answer

$$\frac{125y^6$}{64x$$^{18}$$}$$

Question 18

Which of the following is the correct simplification of $$(w^2 + w$$ - $$1)(w^2 + 6w - 8$$)$$?

Accepted Answer

$$w^4$$ + $$7w^3$$ - $$3w^2 - 14w + 8$

Question 19

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial population is $$3.4 	imes 10^9$ and after t$ hours the population is P = 3.4$$ 	imes $$10^9$$ 	imes 2^t$$, what is the population after 3 hours, in scientific notation?

Accepted Answer

$$2.72 	imes 10$$^{10}$$

Step-by-Step Guidance for MAT-105A-DE Chapters 4–6 Study Guide (Beginning & Intermediate Algebra)

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