Exponents

Exponents

​Raised to the power of...

​Exponent: A number that tells how many times a base is used as a factor.

​Base: the number that is to be multiplied

​Exponential form: when you write the number with a base and exponent

Multiple Choice

Which number is the EXPONENT?
4^{2 =} 16

• 4

• 2

• 16

• not here

​Expanded form: When you show the base and the exponent as a multiplication problem

​As you can see: exponents are just a way to show repeated multiplication

​evaluate: a fancy math way of saying solve the problem

Multiple Choice

Which number is the BASE?
2³ = 8

• 2

• 3

• 8

Multiple Choice

$$2^5$$  

What is the correct equation to solve this problem?

• 2 x 5

• 2 x 2 x 2 x 2 x 2

Multiple Choice

Which is equivalent to 5 x 5 x 5 x 5

• 5³

• 5⁴

• 4⁵

• 5⁵

Multiple Choice

How do you use exponents to represent numbers?

• repeated multiplication

• repeated addition

• repeated subtraction

• repeated division

​Dealing with negative numbers

​ALWAYS use parenthesis to raise a negative number to a power

​What the exponent touch is what is repeated

Multiple Choice

Which of the following is correct?

• $$-3^3=-3\cdot-3\cdot-3$$

• $$\left(-3\right)^3=-3\cdot-3\cdot-3$$

Multiple Choice

Which of the following is correct?

• $$-a^4=-\left(a\cdot a\cdot a\cdot a\right)$$

• $$-a^4=-a\cdot-a\cdot-a\cdot-a$$

• $$\left(-a\right)^4=-\left(a\cdot a\cdot a\cdot a\right)$$

Math Response

Evaluate

$$-3^2=$$

Type answer here

Correct Answer: -9

Deg^°

Rad

Math Response

evaluate

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

Type answer here

Correct Answer: 16

Deg^°

Rad

​ANY number raised to the 0 (zero) power equals 1

Math Response

What is $$2,304,459^0$$ ?

Type answer here

Correct Answer: 1

Deg^°

Rad

Multiple Choice

Simplify (34x⁵y⁶z^-7)⁰

• 34x⁵y⁶ / z⁷

• 34x⁵y⁶ / x^-7

• 0

• 1

​NEGATIVE EXPONENTS

​Honors class only

​"Fixing" negative exponents

​Turn a negative exponent into a positive exponent by using the multiplicative inverse.

​The number you would multiply the original by to make the product 1 (one)

Match

Match the following with their multiplicative inverse.

• $$4$$

• $$-\frac{1}{2}$$

• $$\frac{2}{5}$$

• 2

• $$\frac{8}{7}$$

-2

• $$\frac{1}{4}$$

• -2

• $$\frac{5}{2}$$

• $$\frac{1}{2}$$

• $$\frac{7}{8}$$

​"Fixing" negative exponents

Multiple Choice

Write without negative exponent 2^-1

• 
  $$\frac{1}{2^1}$$

• $$\frac{2^1}{1}$$

• $$-2^1$$

• $$-\ \frac{1}{2^1}$$

Multiple Choice

Rewrite using a positive exponent.
w^-13

• -w¹³

• ¹/_w¹³

• - ¹/_w¹³

• w¹³

Multiple Choice

Simplify the following expression: 
xy^-7

• $$xy^7$$

• $$\frac{x}{y^7}$$

• $$\frac{x^7}{y}$$

• $$x^7y$$