Ch 8 A#3 laws of exponents - add, subtract, and multiply

There are special ways of simplifying powers when

their bases are the same. These tricks can be used as
a shortcut and are known as the “Laws of Exponents.”

Laws of Exponents

Base vs. Exponent

Multiplying With Exponents

Multiplying With Exponents

then:

16,777,216

Dividing With Exponents

Dividing With Exponents

xᐧxᐧxᐧxᐧxᐧxᐧxᐧxᐧx
xᐧxᐧxᐧxᐧxᐧx

x3

Raising a Power

RULE:

When the exponent is on the OUTSIDE of the parenthesis, use the Distributive Property to multiply each
base exponent times the exponent on the outside.

Raising a Power

then:

1048,576

RULE:
When raising an exponential expression to another exponent on the outside,
multiply the exponents together.

Raising a Power

Multiple Choice

$$\left(4^2\right)^4$$

• $$4^{12}$$

• $$4^6$$

• $$4^3$$

• $$4^8$$

Multiple Choice

$$\left(3^3\right)^3$$

• $$3^{16}$$

• $$3^9$$

• $$3^{12}$$

• $$3^6$$

Multiple Choice

$$\left(a^3\right)^4$$

• $$4a^3$$

• $$a^7$$

• $$3a^4$$

• $$a^{12}$$

Multiple Choice

$$\left(m^7\right)^2$$

• $$m^{14}$$

• $$m^9$$

• $$2m^7$$

• $$m^5$$

Multiple Choice

$$\left(4m\right)^2$$

• $$8m^2$$

• $$16m^2$$

• $$4m^2$$

• $$16m$$

Multiple Choice

$$\left(3a^2\right)^4$$

• $$81a^8$$

• $$12a^6$$

• $$81a^2$$

• $$3a^8$$

Multiple Choice

$$2b^4\cdot4b^2$$

• $$6b^6$$

• $$8b^6$$

• $$6b^8$$

• $$2b^2$$

Multiple Choice

$$r^3\cdot3r\cdot5r^2$$

• $$8r^5$$

• $$15r^5$$

• $$15r^6$$

• $$8r^6$$

Multiple Choice

$$\frac{2x^2}{4x^3}$$

• $$2x$$

• $$\frac{1}{2x}$$

• $$\frac{2}{x}$$

• $$\frac{x^5}{2}$$

Multiple Choice

$$\frac{3k^5}{4k^3}$$

• $$\frac{k^2}{1}$$

• $$\frac{3}{4k^2}$$

• $$\frac{3k^2}{4}$$

• $$\frac{3k^8}{4}$$

Multiple Choice

$$3yx^4\cdot x^4y^4$$

• $$3y^5x^8$$

• $$yx^{16}$$

• $$3x^8y^4$$

• $$4yx^4$$

Multiple Choice

$$4m^2n^4\cdot4nm^4$$

• $$8m^6n^4$$

• $$4m^2n^3$$

• $$4m^5n^3$$

• $$16m^6n^5$$

Multiple Choice

$$\frac{3a^3b^2}{ab^4}$$

• $$3a^2b^2$$

• $$\frac{2a}{b^2}$$

• $$\frac{3a^2}{b^2}$$

• $$2a^4$$

Multiple Choice

$$\frac{2nm^4}{6m^4n^2}$$

• $$\frac{1}{3n}$$

• $$\frac{1}{4n}$$

• $$\frac{4}{n}$$

• $$\frac{3m^4}{4n^3}$$

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Solve the system of equations.

• A

• B

• C

• D

Multiple Choice

Solve the system of equations.

• A

• B

• C

• D

Multiple Choice

Find the missing side length

• A

• B

• C

• D

Multiple Choice

Find the missing side length

• A

• B

• C

• D

Multiple Choice

Solve the system by graphing.

• A

• B

• C

• D

Multiple Choice

Solve the system by graphing

• A

• B

• C

• D