Unit 2 Review (Exponent Properties)

What is the BASE in the exponent below?

4³

• 4

• 3

• 4³

• 64

Answer explanation

The base is the larger number that will be repeatedly multiplied by itself.

Which number is the EXPONENT?

4^{2 =} 16

• 4

• 2

• 16

Answer explanation

The exponent is the number smaller in size to the top right of the base. It indicates how many times the base number will be multiplied by itself.

Anything raised to a power of zero is always:

• 0

• 1

• itself

• negative

Answer explanation

Any power involving a zero exponent always has an overall value of 1.

Informal Proof #1:

$x^0$
$=1\cdot x^0$ (multiplying by zero x's)
$=1$

Informal Proof #2:
$x^0$
$=x^{5-5}$ (0 rewritten as a difference of 5 and 5)
$=\frac{x^5}{x^5}$ (Dividing powers property)
$=1$ (anything divided by itself has a value of 1)

Rewrite using a positive exponent.

g^-7

• ¹/_g⁷

• g⁷

• ¹/_g^-7

• -g⁷

Answer explanation

$g^{-7}=\frac{1}{g^7}$

Informal Proof:
$g^{-7}$

$=g^{0-7}$ (-7 rewritten as difference of 0 and 7)

$=\frac{g^0}{g^7}$ (dividing powers property)

$=\frac{1}{g^7}$ (a power with a zero exponent has a value of 1)

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

• add

• subtract

• multiply

• divide

Answer explanation

When multiplying powers, we add the exponents.

Informal Proof:

 $x^3x^5$                                                                  
 $=\left(x\cdot x\cdot x\right)\cdot\left(x\cdot x\cdot x\cdot x\cdot x\right)$  expanded form
 $=x^{3+5}$   total number of x's being multiplied      
 $=x^8$                                                                             

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

• add

• subtract

• multiply

• divide

Answer explanation

When dividing powers, we subtract the exponents.

Informal Proof:

 $\frac{x^6}{x^2}$                                                           

 $=\frac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}$   expanded form     

 $=\frac{x\cdot x\cdot x\cdot x}{1}$   two sets of x's cancel out

"I multiplied by 6 x's, but divided 2 of them away."
 $=x^{6-2}$                                                            
 $=x^4$                                                                

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

• add

• subtract

• multiply

• divide

Answer explanation

When raising a power to another power, we multiply the exponents.

Informal Proof:

$\left(x^3\right)^4$
$=\left(x^3\right)\cdot\left(x^3\right)\cdot\left(x^3\right)\cdot\left(x^3\right)$ expanded form for outer exponent
$=\left(x\cdot x\cdot x\right)\cdot\left(x\cdot x\cdot x\right)\cdot\left(x\cdot x\cdot x\right)\cdot\left(x\cdot x\cdot x\right)$ expanded form for inner exponent
$=x^{3+3+3+3}$ total number of x's being multiplied
$=x^{\left(3\right)\left(4\right)}$
$=x^{12}$

Tags

CCSS.HSA.APR.A.1

Which of the following expressions is equivalent to (2x)³ ?

• (2x)(2x)(2x)

• 2(x)(x)(x)

• 2x + 2x + 2x

• 2x⋅3

Answer explanation

$\left(2x\right)^3$

"2x three times"

$=\left(2x\right)\left(2x\right)\left(2x\right)$

Enter a value to replace the "?" to make the equation below true:

 $\left(x^5\right)^{\ ^?}=x^{45}$ 

Answer explanation

 $\left(x^5\right)^9=\ x^{5\cdot9}\ =x^{45}$  

(r⁴)⁶

• 10r

• $r^{10}$
  

• 24r

• $r^{24}$
  

Answer explanation

$\left(r^4\right)^6$
$=\left(r^4\right)\left(r^4\right)\left(r^4\right)\left(r^4\right)\left(r^4\right)\left(r^4\right)$
$=r^{4\cdot6}$
$=r^{24}$

Tags

CCSS.HSA.APR.A.1