Rules of Exponents

Product Rule

100

What is the Product Rule?

Same Base, ADD the exponents

200

what is 6⁴ x 6²⁼

6⁸

300

8¹¹ x 8 ⁴=

8¹⁵

400

4⁸ x 4⁸⁼

4¹⁶

500

1⁵ x 1³ x 1⁶⁼

1¹⁴

Quotient Rule

100

What is the quotient rule?

Same Base, Subtract Exponents

200

10⁶ divided by 10^{2 =}

10⁴

300

8⁵  divided by 8⁴⁼

8¹

400

2⁴ divided by 2²?

2²

500

4¹⁰ divided by 4⁴

4⁶

Power Rule

100

What is the power rule?

Same Base, multipply the exponents

200

(2⁶)⁴=?

2²⁴

300

(7³)⁴

7¹²

400

(8⁵)⁶

8³⁰

500

(6⁵)⁸

6⁴⁰

Product of Powers Rule

100

What is the Power of Product?

Distribute the outside exponent and multiply by all exponents

200

(ab)³ ?

a³b³

300

(2y⁴)⁶ =?

64y²⁴

400

(xy)^15 = ?

x¹⁵y¹⁵

500

(3xy)² =?

9x²y²

Negative Exponent/Zero Rule

100

What is the rule for a negative exponent?

Make it the reciprocal to make the exponent positive

200

What is the rule for zero exponent?

Anything to the zero power is one

300

2⁰ and bonus problems on the board

 

1

400

4^-2

1/4²

500

7^-5 x 7³= ?

7^{-2 =} 1/49