Exponent Rules

Exponent Rules

Let's learn the rules of exponents

Multiple Choice

Which number is the EXPONENT?
4^{2 =} 16

• 4

• 2

• 16

• not here

Multiple Choice

Which number is the BASE?
2³ = 8

• 2

• 3

• 8

• not here

Multiple Choice

Solve using the product law of exponents

5⁵ ⋅ 5³

• 25⁸

• 5¹⁵

• 25¹⁵

• 5⁸

Multiple Choice

In order to multiply powers with the same base, we add their exponents. 

• True 

• False

Multiple Choice

Simplify

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form. (use product rule)
                                   4³⋅4⁵

• 4⁸

• 16⁸

• 4¹⁵

• 16¹⁵

Multiple Choice

When dividing powers with the same base, you _______________ the exponents.

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

x⁶ / x²

• x⁴

• x¹²

• x³

• x⁸

Multiple Choice

Multiple Choice

• 2 / x²

• -2x²

• 2x²

• 2x¹⁴

Multiple Choice

(2⁸)²

• 2¹⁶

• 2¹⁰

• 2⁶

• 2⁴

Multiple Choice

$$\left(4xy^3\right)^3$$  

• $$x^3y^9$$  

• $$64x^3y^9$$  

• $$12x^4y^6$$  

• $$64x^4y^6$$  

Multiple Choice

$$\left(3u^2v^3\right)^2$$  

• $$9u^4v^5$$  

• $$6u^4v^5$$  

• $$9u^4v^6$$  

• $$6u^4v^6$$  

Multiple Choice

Simplify the exponential expression.

• 2x⁶y¹²

• 2x⁵y⁷

• 8x⁶y¹²

• 8x⁵y⁷

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

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

• $$\frac{x^{10}y^5}{z^{15}}$$

• $$\frac{x^{10}y}{z^{15}}$$

• $$\frac{x^{10}y}{z^3}$$

Simplify

Multiple Choice

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

• $$\frac{9x^6}{25y^2}$$  

• $$\frac{9x^3}{25y}$$  

• $$\frac{9x^6}{5y}$$  

Multiple Choice

In order for an exponential expression to be considered simplified, it can not have any negative exponents.

• True

• False

Multiple Choice

Simplify:  $$x^{-4}=$$  

• $$\frac{1}{-x^4}$$  

• $$-x^4$$  

• $$\frac{1}{x^4}$$  

• $$\left(-x\right)^4$$  

Multiple Choice

Write this expression using positive exponent:

x^-7

• -7

• -7x

• $$\frac{1}{x^7}$$

• $$-\frac{1}{x^7}$$

Multiple Choice

Simplify

• $$\frac{1}{5x^3}$$

• $$\frac{1}{x^5}$$

• $$\frac{-5}{x^3}$$

• $$\frac{5}{x^3}$$

Multiple Choice

Write this expression with only positive exponents:

• a^-2

• a²

• 1/a¹

Multiple Choice

5⁰ = ?

• 5⁰ = 0

• 5⁰ = 1

• 5⁰ = 5

• 5⁰ = -1

Multiple Choice

Simplify (-9)⁰

• -9

• -1

• 1

• 9

Exponent Rules

• Multiple rules can be used in one problem

• Your final answer should be in the simplest form

• Rules can be used in different orders as well

• Powers must be positive to be fully simplified.