Laws of Exponents

Laws of Exponents

What is a POWER?

A simplified notation for repeated multiplication of the SAME number, term, or variable (BASE).

THE EXPONENT tells us how many times the BASE is a FACTOR.

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

Math Response

Simplify:

x⁵ ⋅ x⁷

Type answer here

Correct Answer: x^{12}

Deg^°

Rad

When dividing, SUBTRACT the exponent in the denominator and keep the same base.

​Example 1:   Example 2:   Example 3:  

​Putting it together.

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

Math Response

Simplify the expression. $$\frac{z^9}{z^5}$$

Type answer here

Correct Answer: z^4

Deg^°

Rad

Math Response

Simplify the expression. $$\frac{x^9}{x^5\cdot x^4}$$

Type answer here

Correct Answer: x

Deg^°

Rad

When you have a power raised to an exponent, MULTIPLY the exponents and keep the base.

​Examples:

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

Math Response

(y⁴)⁶

Type answer here

Correct Answer: y^{24}

Deg^°

Rad

Any NUMBER, EXCEPT ZERO with a power/exponent of zero equals 1!

But we CANNOT DIVIDE BY ZERO!!!! And that's exactly the problem!

​Thus it indeteminant or UNDEFINED!

Multiple Choice

Simplify (-1/2)⁰

• 1

• 0

• -1

• -2

Fill in the Blank

Simplify 3⁰

Fill in the Blank

Simplify 0⁰

Negative Exponents

a^-n is the reciprocal of aⁿ.

Multiple Choice

If  $$3^{3\ }=\ 27,\ then\ 3\ ^{-3\ }=\ ?$$  

• $$\frac{1}{3^3}$$  

• -3

• -27

• $$\frac{1}{3^{-3}}$$  

Multiple Choice

$$If\ 2^{-4}=\ \frac{1}{2^4},\ then\ 5^{-2\ }=\ ?$$   

• -25

• $$\frac{1}{5^2}$$  

• -5

• $$\frac{1}{5^{-2}}$$  

Poll

How do you feel about the laws of exponents?

• Most of them confuse me still

• I just need more practice

• Only 1 or 2 laws are giving me trouble

• I fully understand the laws of exponents

Poll

Which laws are still confusing if any?  SELECT ALL THAT APPLY

• Yo Ms. Catt I got this!

• Product Rule $$4^3\times4^2=4^{3+2}$$  

• Power Rule $$\left(4^2\right)^3=4^{2\times3}$$  

• Quotient Rule  $$\frac{4^5}{4^3}=4^{5-3}$$  

• Negative Rule  $$4^{-6}=\frac{1}{4^6}$$