Negative Powers

Presentation

•

Mathematics

•

9th - 12th Grade

•

Hard

Joseph Anderson

FREE Resource

12 Slides • 21 Questions

6.1c- Quotient of Powers, Negative
Exponents, Zero Powers

Obj- To use the rules for Quotient of Powers,
Negative Exponents and Zero Powers

Multiple Choice

Warm-Up #1: Simplify the expression: c⁴⋅c³=

^c12

c⁴⁺³

c⁷

Multiple Choice

Warm-Up #2: Simplify the following expression:

(x⁵)⁴

x⁹

x²⁰

x⁵⁴

Quotient Rule

When dividing powers that have the same base think of dividing as the inverse of multiplying, so what is the inverse of adding?
When you expand x⁵ you have five Xs being multiplied in the numerator and when you expand x² you have two Xs being multiplied in the denominator.
So what happens when you have the Xs in the numerator and Xs in the denominator? Yup! you cross out the matching pairs!
Now what did you end up with?

Quotient Rule Short Cut?!!

When you divide same base powers you keep the base and subtract the exponents.

x⁷/ x²= x^7-2 = x⁵

Multiple Choice

Simplify the following:

$\frac{x^{16}}{x^2}$

$x^{14}$

$x^8$

$x^{18}$

$x^{-8}$

Multiple Choice

Simplify the following:

$\frac{x^9y^7}{x^2y^6}$

$xy^8$

$\left(xy\right)^{24}$

$x^7y$

$x^{11}y^1$

Multiple Choice

Simplify the following:

$\frac{x^7}{x^{-4}}$

$x^{11}$

$x^3$

$x^{-3}$

$x^{-11}$

Multiple Choice

Simplify the following:

$\frac{x^3}{x^8}$

$x^{-5}$

$x^5$

$x^{-3}$

$\frac{1}{x^{11}}$

Negative Exponent Rule

Negative exponents can be written as the reciprocal fraction with a postive exponent

Negative Exponents Examples:

Negative Exponent Rule

Multiple Choice

Simplify x^-7

-7

-7x

$\frac{1}{x^7}$

$-\frac{1}{x^7}$

Multiple Choice

Make this negative exponent positive.

9^-3

9³

$\frac{1}{9^{-3}}$

$\frac{1}{9^3}$

729

Multiple Choice

Rewrite using positive exponents

$\frac{1}{12^{-4}}$

$\frac{1}{12^4}$

$12^{-4}$

$\frac{1}{20,736}$

$12^4$

Multiple Choice

Rewrite using positive exponents.

3x⁻²

$\frac{3}{x^2}$

$\frac{1}{3^2}$

$\frac{x^2}{3}$

-3x²

Zero Exponent

As our exponent increases, we MULTIPLY by the base that many time
So, every time your exponent decreases, we DIVIDE by the base.
When the exponent decreases from 1 to zero, we divide the base by itself and end up with 1

Multiple Choice

Any number written to the 0 power is always 1

Example: 8⁰=1

True

False

Multiple Choice

x⁰

Multiple Choice

Simplify 10⁰

100

Multiple Choice

Simplify -9⁰
(Hint: parenthesis matter)

-1

-9

Extra Examples

Math Response

Answer to #1 $\frac{x^6}{x^2}$

Type answer here

Deg^°

Rad

Math Response

Answer to #2 $13xy^0$

Type answer here

Deg^°

Rad

Math Response

Answer #3 $\left(13xy\right)^0$

Type answer here

Deg^°

Rad

Extra Examples

Math Response

Answer to #4: $2^{-4}$

(Make the exponent positive)

Type answer here

Deg^°

Rad

Math Response

Answer to #5: $\left(-3\right)^{-2}$

Type answer here

Deg^°

Rad

Math Response

Answer to #6: $\frac{y^5}{y^2}$

Type answer here

Deg^°

Rad

Poll

How is your understanding of this topic?

6.1c- Quotient of Powers, Negative
Exponents, Zero Powers

Obj- To use the rules for Quotient of Powers,
Negative Exponents and Zero Powers

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