Describe the pattern in the following example.

35

32= =33=3• 3• 3

Division Rule - When dividing two powers with the same base, subtract the exponents

3• 3• 3• 3• 33• 3

67

64=67−4 = 63

a9

a3=a9−3 = a6

x5y7

x2y5= x5

x2⎛

⎝⎜⎞

⎠⎟y7

y5

⎛

⎝⎜⎞

⎠⎟=x5−2y7−5 =x3y2

Describe the pattern in the following example

3

5⎛⎝⎜

⎞⎠⎟

2

=3

5⎛⎝⎜

⎞⎠⎟3

5⎛⎝⎜

⎞⎠⎟

=3• 3

5 • 5=32

52

Power of Quotient Rule - The power of a quotient is equal to the power of the numerator divided by the power of the denominator

42

33⎛

⎝⎜⎞

⎠⎟

3

=42( )

3

33( )3 =

46

39

3p2

4

⎛

⎝⎜⎞

⎠⎟

3

=3p2( )

3

43=33 p6

43

Rule – The power of any non-zero number to the zero power is equal to one!

(Don’t believe me… watch this!!!)

x4

x4=x4−4 =x0

Or….x4

x4=1

Therefore…

1

52=5−2

53

55

5 • 5 • 55 • 5 • 5 • 5 • 5

1

5 2

53−5

5−2

For any non-zero number a and any integer n, a-n is the reciprocal of an.

a−n =1an

x−3 =1

x3

a−3b2c−2

d−3=

1

a3⎛⎝⎜

⎞⎠⎟b2

1

⎛

⎝⎜⎞

⎠⎟1

c2⎛⎝⎜

⎞⎠⎟d 3

1

⎛

⎝⎜⎞

⎠⎟=a−3

1

⎛

⎝⎜⎞

⎠⎟b2

1

⎛

⎝⎜⎞

⎠⎟c−2

1

⎛

⎝⎜⎞

⎠⎟1

d−3⎛⎝⎜

⎞⎠⎟

=b2d 3

a3c2