A.2 Laws of Exponents

A.2 Laws of Exponents Review

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What is an exponent?

A simplified notation for repeated multiplication of the same number, term, or variable.

Multiple Choice

How do you use exponents to represent numbers?

• repeated multiplication

• repeated addition

• repeated subtraction

• repeated division

Multiple Choice

Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7

?

• 7⁵

• 7⁶

• 6⁷

• 7⁷

When multiplying, ADD the exponents and keep the same base.

Multiple Choice

According to exponent rules, when we multiply the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form.

4³⋅4⁵

• 4⁸

• 16⁸

• 4¹⁵

• 16¹⁵

Multiple Choice

Simplify:

b² ⋅ b⁴

• b⁸

• b⁶

• b²

• 2b⁶

When dividing, SUBTRACT the exponent in the denominator (bottom) and keep the base.

Multiple Choice

According to exponent rules, when we divide the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵

• 9⁹

• 1⁵

• 9^-5

Multiple Choice

Simplify the expression.

• 7⁶
• 7^-5
• 1/7⁵
• 7⁵

When you have an exponent raise to an exponent, MULTIPLY the exponents.

Multiple Choice

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Choice

(r⁴)⁶

• 10r
• r¹⁰
• 24r
• r²⁴

Anything with a power/exponent of zero equals 1!

Multiple Choice

Simplify (-1/2)⁰

• 1

• 0

• -1

• -2

Multiple Choice

$$\left(2xy\right)^5$$  

• $$2x^5y^5$$  

• $$2^5x^5y^5$$  

• $$2xy^5$$  

• $$2\left(x^5y^5\right)$$  

Multiple Choice

Simplify: (3x²)³

• 27x⁶
• 9x⁶
• 3x⁶
• 9x⁵

Multiple Choice

$$\left(3x^4\right)^5$$  

• $$15x^9$$  

• $$15x^{20}$$  

• $$243x^{20}$$  

• $$243x^9$$  

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

• $$\frac{x^{10}y^5}{z^{15}}$$

• $$\frac{x^{10}y}{z^{15}}$$

• $$\frac{x^{10}y}{z^3}$$

Multiple Choice

$$\left(\frac{a^3}{b^5}\right)^4$$  

• $$\frac{a^{12}}{b^{20}}$$  

• $$\frac{a^7}{b^5}$$  

• $$\frac{a^7}{b^9}$$  

• $$a^{12}b^{20}$$  

​Some text here about the topic of discussion.

​Mixed Exponent Laws

​

​Product and Quotient Laws of Exponents

Multiple Choice

$$\frac{x^3\cdot x^4}{x^2}$$  

• $$\frac{x^7}{x^2}$$  

• $$\frac{1}{x^{10}}$$  

• $$x^5$$  

• $$x^{-5}$$  

Power of a Power and Quotient Laws of Exponents

Multiple Choice

Which expression is equivalent to the expression for all values of q where the expression is defined?

• q²⁷

• 1/q²⁷

• q³

• 1/q³

Multiple Choice

Which is greater, $$2654^0$$  or $$5^0$$  ?

• $$2654^0$$

• They are the same

• $$5^0$$

• Zero is greater

Multiple Choice

$$\left(3x^4\right)^5$$  

• $$15x^9$$  

• $$243x^{20}$$  

• $$15x^{20}$$  

• $$243x^9$$  

Match

Match the correct processes for each type of exponent problem.

• Add the Exponents
• Subtract the Exponents
• Multiply the Exponents
• Always equal to 1
• Take the reciprocal of the factor

Multiplying Like Bases

Dividing Like Bases

Power Raised to a Power

Zero Property

Negative Exponents

• Multiplying Like Bases

• Dividing Like Bases

• Power Raised to a Power

• Zero Property

• Negative Exponents

Multiple Choice

Multiply: $$-4e^5\cdot2e^8$$

• -8e⁴⁰

• -2e¹³

• -8e¹³

• -2e⁴⁰

Multiple Choice

$$x^5\left(x^2\right)$$  

• $$x^7$$  

• $$x^{14}$$  

• $$x^3$$  

• $$x^{-3}$$  

Multiple Choice

$$\left(7x^3\right)^0$$  

• 1

• 7

• $$21x^3$$  

• $$x^{10}$$  

Multiple Choice

$$y^3\cdot y\cdot y^4$$  

• $$y^{12}$$  

• $$y^8$$  

• $$y^{-1}$$  

• $$y^{11}$$  

Multiple Choice

Multiply: $$\left(-2e^3g^2\right)\left(5eg^4\right)$$  

• $$3e^3g^8$$  

• $$3e^4g^6$$  

• $$-10e^3g^8$$  

• $$-10e^4g^6$$  

Multiple Choice

$$b^{-4}\cdot b^4$$  

• $$b^{-8}$$  

• $$b^{-16}$$  

• 1

• $$b^8$$  

Multiple Choice

$$7x^0$$  

• 1

• 7

• $$x^7$$  

• $$x^{-7}$$  

Multiple Choice

$$7x^3y^2\cdot5xy^9$$  

• $$12x^4y^{11}$$  

• $$35x^4y^{11}$$  

• $$35x^3y^{11}$$  

• $$12x^3y^{11}$$  

Multiple Choice

Multiply: 3i² ⋅ 4i⁴ ⋅ 2i⁵

• 24i¹¹

• 9i⁴⁰

• 13i¹³

• i²²

Multiple Choice

$$\left(z^5\right)^5$$  

• $$z^{10}$$  

• 1

• $$z^{25}$$  

• 0

Multiple Choice

$$\frac{1}{a^{-5}}$$  

• $$a^{-5}$$  

• $$\frac{a}{5}$$  

• $$a^5$$  

• $$\frac{5}{a}$$  

Multiple Choice

$$\left(b^7\right)^2$$  

• $$b^{49}$$  

• $$b^5$$  

• $$b^9$$  

• $$b^{14}$$  

Drag and Drop

Anything raised to a power of zero is always: 

Placeholder

Drag these tiles and drop them in the correct blank above

1

0

itself

negative

Multiple Choice

$$\left(m^{-8}\right)^{-3}$$  

• $$m^{-24}$$  

• $$m^{24}$$  

• $$m^{11}$$  

• $$m^{-11}$$  

Multiple Choice

$$k^{-6}$$  

• $$\frac{k}{6}$$  

• $$\frac{6}{k}$$  

• $$k^6$$  

• $$\frac{1}{k^6}$$  

Multiple Choice

$$\left(2ab\right)^5$$  

• $$10ab$$  

• $$10a^5b^5$$  

• $$32a^5b^5$$  

• $$32ab$$  

Multiple Choice

$$\left(7e^3\right)^0$$  

• 1

• 7

• $$21x^3$$  

• $$x^{10}$$  

Multiple Choice

$$\left(m^7\right)^4\cdot m^3$$  

• $$m^{28}$$  

• $$m^{14}$$  

• $$m^{28}m^3$$  

• $$m^{31}$$  

Multiple Choice

$$\left(-7x^2\right)\left(4x^4\right)$$  

• $$-28x^8$$  

• $$-28x^6$$  

• $$-3x^8$$  

• $$-3x^6$$  

Multiple Choice

$$p^2\cdot\left(p^5\right)^2$$  

• $$p^{12}$$  

• $$p^9$$  

• $$p^8$$  

• $$p^{10}$$  

Drag and Drop

According to exponent rules, when we raise an exponent to another exponent $$Example:\ \left(2x^3\right)^2$$   we the exponents.

Placeholder

Drag these tiles and drop them in the correct blank above

multiply

add

subtract

divide

Multiple Choice

$$\frac{x^5}{x^2}$$  

• $$x^3$$  

• $$x^{10}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

Multiple Choice

$$\frac{x^8}{x^5}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

• $$x^{13}$$  

• $$x^{40}$$  

Multiple Choice

$$\frac{c^4}{c^8}$$  

• $$c^{12}$$  

• $$c^{-4}$$  

• $$\frac{1}{c^4}$$  

• $$\frac{1}{c^{12}}$$  

Multiple Choice

• a⁷
• a¹⁰
• a³
• a^-3

Multiple Choice

$$\frac{5x^{-4}}{x^{-9}}$$  

• $$5x^5$$  

• $$5x^{-13}$$  

• $$\frac{5}{x^5}$$  

• $$\frac{1}{5x^5}$$  

Multiple Choice

$$\left(-2x^3y^2\right)\left(5xy^4\right)$$  

• $$3x^3y^8$$  

• $$3x^4y^6$$  

• $$-10x^3y^8$$  

• $$-10x^4y^6$$  

Multiple Choice

$$\frac{x^3\cdot x^4}{x^2}$$  

• $$\frac{x^7}{x^2}$$  

• $$\frac{1}{x^{10}}$$  

• $$x^5$$  

• $$x^{-5}$$  

Multiple Choice

$$\left(3i^4\right)^3$$  

• $$15i^9$$  

• $$27i^{12}$$  

• $$15i^7$$  

• $$243i^9$$  

Multiple Choice

$$\left(\frac{6}{z^4}\right)^3$$  

• $$\frac{18}{z^4}$$  

• $$\frac{18}{z^{12}}$$  

• $$\frac{216}{z^{12}}$$  

• $$\frac{6}{z^{12}}$$  

Multiple Choice

$$4z^4\cdot6z^{-6}$$  

• $$\frac{24}{z^2}$$  

• $$24z^{-24}$$  

• $$\frac{10}{z^2}$$  

• $$10z^{-24}$$  

Multiple Choice

$$\left(\frac{a^3}{b^5}\right)^4$$  

• $$\frac{a^{12}}{b^{20}}$$  

• $$\frac{a^7}{b^5}$$  

• $$\frac{a^7}{b^9}$$  

• $$a^{12}b^{20}$$  

Drag and Drop

According to exponent rules, when we divide terms we ​​

Placeholder

the exponents.

Drag these tiles and drop them in the correct blank above

Subtract

Multiply

Divide

Add

Multiple Choice

$$\left(\frac{3x^4}{y^6}\right)^5$$  

• $$\frac{15x^{20}}{y^{30}}$$  

• $$\frac{3x^{20}}{y^6}$$  

• $$\frac{243x^{20}}{y^{30}}$$  

• $$\frac{243x^9}{y^{11}}$$  

Multiple Choice

$$\left(3xy\right)\left(xy\right)$$  

• $$x^2y^2$$  

• $$3xy$$  

• $$3x^2y^2$$  

• $$\frac{xy}{3xy}$$  

Multiple Choice

$$\left(\frac{3x^7}{2y^{12}}\right)^0$$  

• $$\frac{x^7}{y^{12}}$$  

• 0

• $$\frac{3x^7}{2y^{12}}$$  

• 1

Multiple Choice

Simplify the exponential expression:

• 10x^-2
• 2x²
• 2x¹²
• 10x¹²

Multiple Choice

$$3x^{-2}y^{-5}$$  

• $$3x^{-2}y^{-5}$$  

• $$\frac{3}{x^2y^5}$$  

• $$\frac{1}{x^2y^5}$$  

• $$3xy^{-7}$$  

Multiple Choice

• -6c⁵

• -6c

• 6c

• -6c⁶

Multiple Choice

$$\left(f^{-3}g^5h^8\right)^{-3}$$  

• $$f^9g^5h^8$$  

• $$f^{-6}g^2h^5$$  

• $$\frac{g^2h^5}{f^6}$$  

• $$\frac{g^9}{g^{15}h^{24}}$$