Exponent Rules

Exponent Rules

Review Rules for Simplifying Expressions with Exponents

Important Exponent Rules

Anything to the zero power is ______

3⁰ = ___

Multiple Choice

Simplify (-9)⁰

• -9
• -1
• 1
• 9

Multiple Choice

Simplify 10⁰

• 10
• 1
• 0
• 100

Multiple Choice

*Be careful* :)

(-4r³s⁵)⁰(3b⁴c²d)

• 1

• -12b⁴c²d

• 3b⁴c²d

• 0

Some phrases to remember what Negative Exponents mean:

"Make a Fraction"

"Divide"

"Move to the denominator"

Multiple Choice

Rewrite using a positive exponent.
w^-13

• -w¹³
• ¹/_w¹³
• ¹/_w^-13
• w¹³

Multiple Choice

Rewrite using a positive exponent.
7^-10

• ¹/_7¹⁰
• 7¹⁰
• ¹/_7^-10
• -70

Multiple Choice

Anything raised to a power of zero is always:

• 0

• 1

• itself

• negative

Multiple Choice

Simplify (evaluate completely):

5^-2

• -10

• 1/25

• 1/(5)²

• -1/10

Multiple Choice

Simplify the following expression:

-9⁰

• -9

• 0

• -1

• 1

Multiple Choice

Rewrite using positive exponents

• 2⁴

• 1/2⁴

• 4²

• 1/4²

When Simplifying Expressions involving Multiplication

Remember "Multiply the Coefficients and ADD the Exponents"

If the Exponent is OUTSIDE of ( ) then you MULTIPLY it by ALL exponents INSIDE ( )

Multiple Choice

HINT:  When you multiply like bases KEEP the base!!

 $5^2\cdot5^4$  

•  $5^6$  

•  $5^8$  

•  $25^6$  

•  $25^8$  

Multiple Choice

According to exponent rules, when we multiply two exponent expressions with the same base we _______ the exponents and KEEP the base.

Example: c⁶ ⋅ c⁴

• add

• subtract

• multiply

• divide

Multiple Choice

How do you solve:

(2x⁵)(6x⁴)

• MULTIPLY coefficients

  KEEP base

  MULTIPLY exponents

• DIVIDE coefficients

  KEEP base

  SUBTRACT exponents

• MULTIPLY coefficients

  CHANGE base

  ADD exponents

• MULTIPLY coefficients

  ADD exponents

Multiple Choice

 $3^7\cdot3^7$  

•  $9^{49}$  

•  $3^{14}$  

•  $3^{49}$  

•  $9^{14}$  

Multiple Choice

Simplify:  $\left(2a^3b^4c^3\right)^{ }\cdot\left(4a^2bc^3\right)$  

•  $16a^8b^9c^9$  

•  $8a^5b^5c^6$  

•  $8a^6b^5c^6$  

•  $16a^5b^5c^6$  

Multiple Choice

Simplify:  $3n^5\cdot5n^{10}$  

•  $15n^5$  

•  $8n^{15}$  

•  $15n^{50}$  

•  $15n^{15}$  

Multiple Choice

Simplify the expression.
x⁴ (x¹²)

• x³
• x⁴⁸
• x¹⁶
• x⁸

Multiple Choice

Simplify to an equivalent expression BUT leave in exponent form.
                                   4³⋅4⁵

• 4⁸
• 16⁸
• 4¹⁵
• 16¹⁵

Multiple Choice

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

• add
• subtract
• multiply
• divide

Multiple Choice

(2⁸)²

• 2¹⁶

• 2¹⁰

• 2⁶

• 2⁴

Multiple Choice

Simplify
(3x³y⁵)⁴

• 3x¹²y²⁰
• 81x¹²y²⁰
• 12x¹²y²⁰
• 81x⁷y⁹

Multiple Choice

Mix it together!

-3xy³ . (4xy)²

• -12x³y⁵

• -48x²y⁴

• -48x³y⁵

• -12x²y⁶

Multiple Choice

(a⁴b¹⁹c²¹d^-14)⁰

• 1
• 0
• a⁴b¹⁹c²¹d^-14
• a^-4b^-19c^-21d¹⁴

Multiple Choice

6y²⋅(2y²)³

• 48y⁸
• 12y⁸
• 48y⁷
• 12y⁷

Multiple Choice

Simplify:     (2x⁴y⁵)(-3x²y⁷)

• 6x⁶y¹²
• -1x⁶y^-2
• -6x²y²
• -6x⁶y¹²

Multiple Choice

(a³b)⁴

• a¹²b⁴
• a⁷b⁵
• a³b⁴
• ab⁸

Multiple Choice

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

• 2x¹⁸y⁶

• 64x¹⁸y⁶

• 64x³y⁶

• 2x³y⁶