Negative Exponents

​Negative Exponents

​Negative Exponents

​Remember if an exponent is negative, you simply just: 1.) "change levels" and...
2.) make the the exponent positive.

​For Example:
Simplify using only positive exponents.

- Notice how the exponent is positive now!

Multiple Choice

Simplify using only positive exponents: $$5^{-8}$$

• $$5^8$$

• $$\frac{1}{5^8}$$

• $$\frac{1}{5^{-8}}$$

• $$-5^8$$

Multiple Choice

Simplify using only positive exponents: $$y^{-3}$$

• $$3y$$

• $$-y^3$$

• $$\frac{1}{y^3}$$

• $$\frac{1}{y^{-3}}$$

Multiple Choice

Simplify using only positive exponents: $$a^{-1}$$

• $$a$$

• $$-a$$

• $$\frac{1}{a^{-1}}$$

• $$\frac{1}{a}$$

​Negative Exponents

​If the exponent is reduceable, reduce it!

​For Example:
Simplify using only positive exponents.

 

- Since we know that 2² = 4, change it to 4!

Multiple Choice

Simplify using only positive exponents: $$3^{-2}$$

• $$-9$$

• $$\frac{1}{-9}$$

• $$\frac{1}{9}$$

• $$\frac{1}{6}$$

Multiple Choice

Simplify using only positive exponents: $$2^{-3}$$

• $$\frac{1}{8}$$

• $$\frac{1}{-8}$$

• $$-8$$

• $$\frac{1}{6}$$

​Negative Exponents

​Also, you only move the base that has a negative exponent attached to it.

​For Example:

- ​The "a" is the only base with a negative exponent.

- So only move the "a" and not the "b".

Multiple Choice

Simplify using only positive exponents: $$xy^{-3}$$

• $$\frac{x}{y^3}$$

• $$\frac{1}{xy^3}$$

• $$\frac{x}{y^{-3}}$$

• $$xy^3$$

Multiple Choice

Simplify using only positive exponents: $$a^{-2}b$$

• $$-a^2b$$

• $$\frac{b}{a^2}$$

• $$\frac{1}{a^2b}$$

• $$\frac{a^2}{b}$$

Multiple Choice

Simplify using only positive exponents: $$x^{-1}y^3$$

• $$-xy^3$$

• $$\frac{y^3}{x}$$

• $$\frac{x}{y^3}$$

• $$xy^3$$

​Negative Exponents

​If the base with the negative exponent is on the bottom, then "change levels" by bringing it up:

​For Example:

• Move it up!

Multiple Choice

Simplify using only positive exponents: $$\frac{1}{y^{-2}}$$

• $$-2y$$

• $$-y^2$$

• $$y^2$$

• $$y^{-2}$$

Multiple Choice

Simplify using only positive exponents: $$\frac{1}{a^{-1}}$$

• $$a$$

• $$-a$$

• $$\frac{1}{a}$$

• $$\frac{1}{-a}$$

​Negative Exponents

​If there are more than one bases with negative exponents, move and switch levels for each of them.

​For Example:

- Move the "x" and the "y" only!
- The "x" goes down and the "y" moves up.

- The "z" did not move as it didn't have a negative exponent.

Multiple Choice

SImplify using only positive exponents: $$a^{-2}bc^{-1}$$

• $$\frac{bc}{a^2}$$

• $$-a^2bc$$

• $$\frac{a^2b}{c}$$

• $$\frac{b}{a^2c}$$

Multiple Choice

SImplify using only positive exponents: $$\frac{a^3b^{-2}}{c^{-5}}$$

• $$\frac{a^3c^5}{b^2}$$

• $$a^3b^2c^5$$

• $$\frac{a^3}{b^2c^5}$$

• $$\frac{b^2c^5}{a^3}$$

Multiple Choice

SImplify using only positive exponents: $$\frac{a^2}{b^{-3}c^{-8}}$$

• $$\frac{b^3c^8}{a^2}$$

• $$a^2b^3c^8$$

• $$\frac{a^2b^3}{c^8}$$

• $$\frac{c^8}{a^2b^3}$$

Match

Match the following:

• $$\frac{a^{-3}b^{-5}}{c^{-1}}$$

• $$\frac{a^3c^{-1}}{b^{-5}}$$

• $$a^{-3}b^{-5}c^{-1}$$

• $$\frac{a^3b^5}{c^{-1}}$$

• $$\frac{1}{a^{-3}b^5c^{-1}}$$

• $$\frac{c}{a^3b^5}$$

• $$\frac{a^3b^5}{c}$$

• $$\frac{1}{a^3b^5c}$$

• $$a^3b^5c$$

• $$\frac{a^3c}{b^5}$$