3/3 - M8 - Exponent, Cube Roots and Square Roots Review

3/3 - M8 - Exponent, Cube Roots and Square Roots Review

By Kimberleigh Carter

ANY NUMBER TO THE POWER OF 0 equals 1

​​Zero Rule

When an exponent is raised to another power you MULTIPLY the exponents.

​​Power Rule

SUBTRACT exponents when dividing with like bases.

​​Dividing Exponents

​

When multiplying like bases ADD the exponents.

​​Product RULE

Exponents

Exponents represent repeated multiplication.

Poll

Is  $$8^3$$  the same thing as  $$8\times3$$  ?

• Yes

• No

Examples:

​

4^2 = 4 times 4 = 16

6^4 = (6) (6) (6) (6) = 1,296

3^2 = 3 * 3 = 9

2^3 = 2 times 2 times 2 = 8​

Exponents tell how many times to multiply the base times its self.

8^3 = 8*8*8 is NOT the same as 8*3

Some text here about the topic of discussion

Poll

Is $$\left(-3\right)^2$$  the same thing as  $$-3^2$$  ?

• Yes

• No

(-3)^2 = 9 but -3^2=-9

Parenthesis include the negative sign!!!​

If there is not a parenthesis the answer WILL BE NEGATIVE!!!!

Multiple Select

Select all the expressions that are equivalent to $$7^2$$ .

• $$14$$  

• $$7\times7$$  

• $$7\times2$$  

• $$49$$  

• $$7+2$$  

Zero Exponents

Any non-zero number raised to the zero power is 1.

Multiple Choice

$$x^0=$$  

• 0

• 1

• x

• -x

Negative Exponents

Negative exponents means the reciprocal of the positive power.

Multiple Select

Select all the expressions that are equivalent to $$4^{-3}$$  .

• $$-12$$  

• $$\frac{1}{64}$$  

• $$-64$$  

• $$\frac{1}{4^3}$$  

• $$64$$  

Squares and Square Roots

Multiple Choice

$$\sqrt{64}=$$  

• $$32$$  

• $$4$$  

• $$8$$  

• $$64^2$$  

Cubes and Cube Roots

Multiple Choice

$$3^3=$$  

• $$9$$  

• $$27$$  

• $$6$$  

• $$12$$  

Multiple Choice

$$^{3\sqrt{8}}$$  

• $$\frac{8}{3}$$  

• $$2$$  

• $$512$$  

• $$5$$  

Multiple Choice

$$x^0=$$  

• 0

• 1

• x

• -x

Multiple Choice

A square poster has an area of 81 square inches. What is the length of each side of the square?

• 3 inches

• 9 inches

• 20.25 inches

• 40.5 inches

Multiple Choice

$$10\times10\times10\times10\times10=$$  

• $$10\times5$$  

• $$10^5$$  

Multiple Choice

What does this symbol represent?

• square root

• divide by 2

• cube root

• greater than or less than

Multiple Choice

$$10^3=$$  

• $$10\times10\times10$$  

• $$10\times3$$  

• $$10+10+10$$  

• 10,000

Poll

Which task do you think is the easiest?

• Determining the area of a square given the side length.

• Determining the volume of a cube given the side length.

• Determining the side length of a square given the area.

• Determining the side length of a cube given the volume,

Multiple Choice

Which number is the BASE? $$2^7$$ =128

• 2

• 7

• 128

• $$2^7$$  

Multiple Select

Which representations are equal to 64?

• 8²

• 32²

• (-8)(-8)

• 4³

• 21³

Multiple Choice

If a number or variable does not have an exponent, we can assume the exponent is:

• 0

• 1

Multiple Choice

Leona is so excited. Her grandma is ordering a cubic hot tub that has a volume of 216 ft³. Her grandma needs to know how long each side is to order trim. What is the length of each side?

• 4 feet

• 6 feet

• 8 feet

• 108 feet

Multiple Choice

$$y^0=$$  

• y

• 0

• 1

• 10

Multiple Choice

Valencia, Saralyn, and Emily are solving math problems to win a race. They need to determine the approximate value of  $$\sqrt{47}$$ . Saralyn insists the value is closer to 7, while Emily is sure it is closer to 8. Valencia thinks the value is closer to 6. Who do you agree with?

• Saralyn 

• Emily

• Valencia

Multiple Choice

$$365^0=$$  

• 0

• 1

• 365

• $$\frac{1}{365}$$  

Multiple Choice

What is the difference between the area of square A and square B.

Square A has side lengths of 5 cm and square B has side lengths of 7 cm.

• 2 cm²

• 4 cm²

• 16 cm²

• 24 cm

• 24 cm²

Multiple Choice

$$x^{-5}$$  =

• $$\frac{1}{x^{-5}}$$  

• $$\frac{1}{x^5}$$  

• $$\frac{x^5}{1}$$  

• $$\frac{x^{-5}}{1}$$  

Multiple Choice

The area of Nisreen's garden is 131 square feet. About how many feet is the length of each side? Round to the nearest whole number!

• 11 feet

• 12 feet

• 13 feet

• 65.5 feet

Multiple Choice

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Listen and solve!!

• 5

• 12

• 125

• 625

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

Multiple Choice

$$m^2\cdot m^6\cdot m=$$  

• $$m^8$$  

• $$m^{12}$$  

• $$m^4$$  

• $$m^9$$  

Multiple Choice

$$x^{-3}\cdot x^7\cdot x^2$$  =

• $$x^6$$  

• $$x^{12}$$  

• $$x^{-42}$$  

• $$x^{-12}$$  

Multiple Choice

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

• Add

• Subract

• Multiply

• Divide

Multiple Choice

$$\frac{x^9}{x^4}$$  =

• $$x^{13}$$  

• $$x^{36}$$  

• $$x^5$$  

• $$x^{-5}$$  

Multiple Choice

$$\frac{x^{17}}{x^8}$$  

• $$x^9$$  

• $$x^{25}$$  

• $$x^{-9}$$  

• $$x^{-25}$$  

Multiple Choice

$$\frac{9x^2}{3x^{ }}=$$  

• $$3x^2$$  

• $$3x$$

• $$9x$$  

• $$6x$$  

Multiple Choice

$$\frac{a^5b^{10}}{a^3b^6}=$$  

• $$a^8b^{16}$$  

• $$a^2b^4$$  

• $$a^{15}b^{60}$$  

• $$a^2b^{16}$$  

Multiple Choice

$$\left(x^5\right)^4$$  

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

• add

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

$$\left(a^3b^5\right)^7$$  =

• $$a^3b^{35}$$  

• $$a^{10}b^{12}$$  

• $$a^8b^8$$  

• $$a^{21}b^{35}$$  

Multiple Choice

$$\left(ab^2\right)^8$$  =

• $$ab^{16}$$  

• $$a^8b^{16}$$  

• $$a^9b^{10}$$  

• $$ab^{10}$$