Exponents - Combining, Multiplying, and Power to a Power

EXPONENTS

• ​Combining

• Multiplying

• Power to a Power​

• Dividing​

x²

​Base

​Exponent (or Power)

​Vocabulary Words

Combining

To combine terms with exponents, the bases and exponents must be exactly the same! Combine the coefficients. You DON'T change the exponents!

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​Example 1: 2x² + 5x² = 7x²

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Example 2: 8a⁵ + 3b³ - 5a⁵ + 4b³ = 3a⁵ + 7b³

Multiple Choice

Simplify.

8x² - 2x²

• 10x²

• 6x²

• 6

• 6x⁴

Multiple Choice

Simplify.

12a⁷ + 4b⁵ - 5a⁷ + 6b⁵

• 16ab¹² - 1ab²

• 17a⁷ + 2b¹⁰

• 7a⁷ + 10b⁵

• 7ab²⁴

Multiplying

When multiplying, you ADD the exponents! (You still multiply the coefficients.)

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Example 1: x³ ​· x⁵ = x⁸

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​Example 2: 5y² · 4y⁷ = 20y⁹

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Example 3: (2a³​b⁵) (-3a⁷b²) = -6a¹⁰b⁷

Multiple Choice

Simplify.

$$g^4\cdot g^3$$   

• $$2g^{12}$$  

• $$g^7$$  

• $$g^{ }$$  

• $$12g$$  

Multiple Choice

Simplify.

-2x² $$\cdot$$  4x³

• -8x⁵

• 2x^-1

• -8x⁶

• -16x⁵

Multiple Choice

Simplify.

(-3a²b⁴c⁶) (-4a⁷b³c⁹)

• -12a⁵bc³

• 12a⁹b⁷c¹⁵

• -7a¹⁴b¹²c⁵⁴

• 12a²b³c⁴

Power to a Power

When you have an exponent raised to another exponent, you must MULTIPLY the exponents. "A power to a power, you multiply!" It is sort of like the distributive property. The exponent on the outside goes to EVERYTHING on the inside of the parentheses!

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​​Example 1: (x³​)² = x⁶

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​Example 2:​ (-2a⁵b⁷)³ = -8a¹⁵b²¹ (Remember (-2)³ means -2 · -2 · -2)

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Multiple Choice

Simplify.

$$\left(x^3y^2\right)^4$$  

• x⁷y⁶

• x¹²y⁸

• x⁸¹y¹⁶

• xy²

Multiple Choice

Simplify.

$$\left(-3a^5b^2c\right)^3$$  

Don't forget c has an exponent of 1

• -9a²bc²

• 9a⁸b⁵c⁴

• -27a¹⁵b⁶c³

• 27abc³

Dividing

​When dividing, you SUBTRACT the exponents! (You still divide the coefficients.)

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Example 1: x⁵/x² = x³ ​​

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​Example 2: 20x⁴y⁷/4xy⁵ = 5x³y²

Multiple Choice

Simplify.

$$\frac{x^{10}}{x^3}$$  

• $$x^{13}$$  

• $$x^7$$  

• $$x^{30}$$  

• $$x^3$$  

Multiple Choice

Simplify.

$$\frac{24x^5y^9}{3x^3y^4}$$  

• $$8x^2y^5$$  

• $$21x^2y^5$$  

• $$27x^2y^5$$  

• $$8x^8y^{13}$$  

Mi​xed Practice

​Here are a few problems that involve more than one step! Use scratch paper!

Multiple Choice

Simplify.

$$\left(\frac{4x^5y^4}{2x^2y^2}\right)^3$$  

• $$32x^{15}y^{12}$$  

• $$8x^9y^6$$  

• $$16x^6y^5$$  

• $$-5x^4y^3$$  

Multiple Choice

Simplify.

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

• $$22x^4y^6$$  

• $$-2x^{12}y^{16}$$  

• $$2x^4y^6$$  

• $$8x^5y^6$$  

Multiple Choice

Simplify.

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

• $$13x^4y^7$$  

• $$-7x^{12}y^9$$  

• $$22x^6y^{10}$$  

• $$5x^6y^{10}$$  

Multiple Choice

Simplify.

$$\frac{\left(2x^2\right)^3\left(3x^4\right)^2}{12x^9}-\ 4x^5$$  

• $$14x^9$$  

• $$124x^{32}$$  

• $$2x^5$$  

• $$32x^{12}$$  

Multiple Choice

Simplify. (Think about it!!!)

$$\left(\frac{156x^{12}y^{15}z^{21}}{36x^9y^{13}z^6}\right)^0\ +\ \ \left(\frac{935x^{23}y^{18}z^{20}}{415x^{19}y^{17}z^{14}}\right)^0$$  

• $$652x^{32}y^{51}z^{12}$$  

• $$216x^{15}y^{19}z^{14}$$  

• $$84x^{28}y^{22}z^{18}$$  

• $$2$$