Rules of Exponents Intro

Exponent Rules, Simplifying Radicals, Rational Exponents

By Shalynne Orth

Multiple Choice

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

• 0

• 1

Multiple Choice

Product Rule

When multiplying exponents with the same base, _______ the exponents.

• subtract

• add

• multiply

• divide

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

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

Zero Rule

Any number raised to the zero power is always__________.

• zero

• one

• exponent

• raised

Multiple Choice

$$y^0=$$  

• y

• 0

• 1

• 10

Multiple Choice

Negative Exponent Rule

When you have a negative exponent, take the reciprocal of the base and exponent. Always get rid of the ____________exponents in an expression.

• zero

• negative

• positive

• ugly

Multiple Choice

$$x^{-5}$$  =

• $$\frac{1}{x^{-5}}$$  

• $$\frac{1}{x^5}$$  

• $$\frac{x^5}{1}$$  

• $$\frac{x^{-5}}{1}$$  

Multiple Choice

Power to a Power Rule

When raising a power to a power, keep the base and ________ the exponents

• postive

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

Power of a Product Rule

When raising a product to a power, __________ the exponents to each factor in the product. Then simplify the expression.

• distribute

• add

• multiply

• divide

Multiple Choice

$$\left(a^3b^5\right)^7$$  =

• $$a^3b^{35}$$  

• $$a^{10}b^{12}$$  

• $$a^8b^8$$  

• $$a^{21}b^{35}$$  

Multiple Choice

Power of a Quotient Rule

When raising a quotient to a power, distribute the _____________ to the numerator and denominator. Then simplify the expression.

• exponent

• numbers

• integers

• name

Multiple Choice

$$\left(\frac{x^4}{x^2}\right)^3$$   Simplify

• $$x^8$$  

• $$x^6$$  

• $$x^3$$  

• $$x^9$$  

Multiple Choice

Simplify

• $$\frac{x^{28}y^{12}}{x^2y}$$

• $$\frac{x^{28}y^{12}}{x^8y^4}$$

• $$x^{20}y^8$$

Multiple Choice

Simplify using your exponent rule(s) (2x³y)⁶

• 2x¹⁸y⁶

• 64x¹⁸y⁶

• 64x³y⁶

• 2x³y⁶

Multiple Choice

Simplify:  (5p⁹q³)(2pq⁷)

• 7p¹⁰q¹⁰
• 10p⁹q²¹
• 10p¹⁰q¹⁰
• 10p⁸q^-4

Multiple Choice

Simplify: 7p⁰

• 7

• 1

• simplified

• 7p

simplifying Radicals

Multiple Choice

√28

• 7√2

• 7√4

• 4√7

• 2√7

Multiple Choice

√125

• 5√5

• 25√5

• 5√25

• 5√2

Multiple Choice

Simplify the following radical: √300

• 3√10
• 2√150
• 100√3
• 10√3

Multiple Choice

Simplify completely:

• 4

• cannot be simplified.

Multiple Choice

Simplify completely:

• cannot be simplified

Rational Exponents and Radicals

Rational Exponents

Converting from "Exponent Form" to "Root Form"

Multiple Choice

Evaluate.

$$25^{\frac{1}{2}}$$  

• 12.5

• 5

• -25

• 25.5

Multiple Choice

Rewrite into exponent form.

$$\sqrt{x^3}$$  

• $$x^{\frac{3}{2}}$$  

• $$x^{\frac{2}{3}}$$  

• $$x^6$$  

• $$\frac{x}{3}$$  

Multiple Choice

Evaluate.

$$16^{\frac{3}{2}}$$  

• 16.32

• 17.5

• 64

• 1632

Multiple Choice

Evaluate

$$32^{\frac{3}{5}}$$  

• 216

• 32.35

• 8

• 32.6

Negative Rational Exponents

Multiple Choice

Simplify.

$$9^{-\frac{3}{2}}$$  

• $$-9.32$$  

• $$-27$$  

• $$\frac{1}{27}$$  

• $$\frac{1}{93}$$