Prealgebra Final Review

Final Review

by Sydnee Jones

​Used to find the distance between 2 coordinates. Label your coordinates before starting!

Multiple Choice

How is the distance formula correctly written:

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$$

• $$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}$$

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$$

• d = $$\sqrt{\left(x\right)^2-\ \left(y\right)^2}$$

Multiple Choice

Find the distance between (-12, 1) and (12, -1).

• 24.05
• 24.06
• 24.07
• 24.08

Multiple Choice

Find the distance between (-5, -8) and (-1, -16).

• 8.9
• 9.8
• 10.3
• 11

Multiple Choice

Find the distance between J and K.

• 8.2
• 7.7
• 9
• 10.2

Multiple Choice

What is the distance between AB

• 0

• 8

• 9

• 7

​Used to find the missing side of a right triangle. The hypotenuse is c, across from the right angle. A and b are legs.

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Choice

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

Multiple Choice

Find the distance of the wall to the ladder.

• 5

• 7

• 9

• 11

Multiple Choice

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled? (PERIMETER)

• 17 miles
• 32 miles
• 37 miles
• 40 miles

​Product Rule: Keep the base, add the exponents

​Quotient Rule: Keep the base, subtract the exponents

​Power Rule: Keep the base, multiply the exponents

​Power to a Fraction Rule: Distribute the power to each power inside the parenthesis.

​Negative Rule: Move the negative exponent and the base attached to the opposite side of the fraction bar. Then change to a positive exponent.

Zero Rule: Anything to the 0 power is 1.

Simple Exponent Rules

Multiple Choice

x⁵⁄x³

• x²
• x
• 1
• x⁸

Multiple Choice

(x⁸)(x^-5)

• x^-40
• x^-13
• x¹³
• x³

Multiple Choice

(t^-6)^-5

• t^-11
• t^-30
• t³⁰
• t¹¹

Multiple Choice

(3x)⁰

• (3x)¹
• 0¹
• 1
• 3x

Multiple Choice

x⁻⁶

• 1 ⁄ x⁶
• x⁶
• -x⁶
• -1 ⁄ x⁶

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

Write this expression using a positive exponent: $$x^{-4}$$  

• $$\frac{1}{x^{-4}}$$  

• $$\frac{1}{x^4}$$  

• $$x^4$$  

• $$\frac{x}{x^4}$$  

Multiple Choice

Simplify: $$x^3\cdot x^7$$  

• $$x^{21}$$  

• $$x^4$$  

• $$x^{10}$$  

• $$x^{-4}$$  

Multiple Choice

Simplify: $$\frac{x^4}{x^6}$$  

• $$x^2$$  

• $$x^{10}$$  

• $$\frac{1}{x^2}$$  

• $$\frac{1}{x^{10}}$$  

Multiple Choice

Evaluate the following: $$2^{-3}$$  

• $$-6$$  

• $$\frac{1}{-6}$$  

• $$\frac{1}{8}$$  

• $$8$$  

Multiple Choice

$$m^2\cdot m^6\cdot m=$$  

• $$m^8$$  

• $$m^{12}$$  

• $$m^4$$  

• $$m^9$$  

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

Can you leave a negative exponent in your answer?

• YES
• NO

Multiple Choice

What rule would you use to simplify the following?

(r⁴)⁶

• Product Rule

• Quotient Rule

• Power Rule

Multiple Choice

What rule would you use to simplify the following?

x⁰

• Power Rule

• Zero Exponent Rule

• Negative Exponent Rule

Multiple Choice

What rule would you use to simplify the following?

x⁻⁶

• Negative Power Rule

• Power Rule

• Zero Exponent Rule

Multiple Choice

What rule would you use to simplify the following? $$5^3$$   $$\times$$   $$5^9$$  

• Power Rule

• Product Rule

• Quotient Rule

Multiple Choice

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

• $$\frac{x^8}{y^{12}}$$  

• $$\frac{x^6}{y^7}$$  

• $$x^8y^{12}$$  

Multiple Choice

$$\left(\frac{2}{3}\right)^4$$  

• $$\frac{8}{12}$$  

• $$\frac{2}{3}$$  

• $$\frac{24}{34}$$

• $$\frac{16}{81}$$  

Adding/Subtracting: Before numbers in scientific notation can be added or subtracted, the exponents must be the same.

Multiplying: When multiplying, multiply the coefficients and add the exponents.

Dividing: When dividing, divide the coefficients and subtract the exponents.​

Scientific Notation

Multiple Choice

Write the answer in scientific notation.
7.3 x 10⁵  +   3.7 x 10⁵  =

• 11.0 x 10⁵
• 1.1 x 10¹⁰
• 1.10 x 10¹¹
• 1.1 x 10 ⁶

Multiple Choice

Write the answer in scientific notation.
4.1 x 10⁵ +   5.5 x 10⁶  =

• 5.91 x 10⁶
• 9.6 x 10⁵
• 9.6 x 10¹¹
• 4.65 x 10⁵

Multiple Choice

Solve:
(2.1×10​²​​) × (3.0×10​⁴)

• 5.1 x 10²
• 6.3 x 10⁶
• 5.1 x 10⁶
• 6.3 x 10⁸

Multiple Choice

Which is the smallest?
1.3 x 10²⁰
2.9 x 10²¹
9.5 x 10³²
8.4 x 10¹⁹

• 1.3 x 10²⁰
• 2.9 x 10²¹
• 9.5 x 10³²
• 8.4 x 10¹⁹

Multiple Choice

Which is the largest?
4.8 x 10^-6 
1.3 x 10²⁰
3.1 x 10^-4
9.2 x 10^-5 
9.5 x 10³²
5.9 x 10^-5
2.9 x 10²¹
8.4 x 10¹⁹

• 9.5 x 10³²
• 3.1 x 10^-4
• 8.4 x 10¹⁹
• 4.8 x 10^-6 

Multiple Choice

Numbers in front of the decimal must be between these two numbers to be in proper scientific notation.

• More than 1, less than 10

• More than 0, less than 10

• More than 1, less than or equal to 10

• More than 0, less than or equal to 10

Multiple Choice

Solve:

(6 x 10⁶) / (2 x 10³)

• 12 x 10³

• 3 x 10⁹

• 1.2 x 10¹⁰

• 3 x 10³

Multiple Choice

Write the answer in scientific notation.
5 x 10⁸ -   3.4 x 10⁸  =

• 2.4 x 10⁸
• 2.4 x 10⁰
• 1.6 x 10⁰
• 1.6 x 10⁸

Multiple Choice

Find the difference
(3.8 x 10⁴) - (2 x 10³)

• 1.8 x 10⁴
• 1.8 x 10¹
• 3.6 x 10¹
• 3.6 x 10⁴

Multiple Choice

(9.6×10^-8)÷(2×10^-15)

• -4.8×10⁷

• 4.8×10⁷

• 4.8×10^-7

• 4.8×10^-23