LAWS OF EXPONENTS

Product Rule -multiplying powers with same bases1. am • an = am+n

52 • 53 = (5•5)(5•5•5)

= 52+3 = 55

55 / 52 = 5•5•5•5•5 = 55-2

5•5 = 53

Quotient Rule -dividing powers with same bases2. am = am – n , a0

an

Examples:

1. x5 • x7 =2. m12n3 • m4n11 =

3. 26b9 = 22b2

4. 78c15/ 74c12 =

Examples:

5. s13t6 • s5t8 = s10t3

6. a11b7 • a14c4d9 = 22 a12b3cd2

7. q5r15• q3r8/q4r12 =

3. am = am – m = a0 , a0

am

Zero Exponent Rule

74 / 74 = 7•7•7•7 = 74-4

7•7•7•7 = 70 =1

4. a– m = 1 , a0

am

Negative Exponent Rule

34 = 3 • 3 • 3 • 3 =34–7

37 3•3•3•3•3•3•3 = 1

33

Examples:

1. p5 • p – 7 =2. t0u– 4 • t4u–1 =

3. 39 s0 = 312s–2

4. 5-3k4/ 54k–6 =

Examples:

5. a–3b– 6 • a5b8 = a–2b2

6. m– 5 n6•2–2m– 3n– 5 = 2–5 m0n– 5• m2n3

7. p–2s– 7• p– 4s8/p–6s0 =

Power of Power

5. (am)n = amn

(52)3 = (5•5)(5•5)(5•5)

=5•5•5•5•5•5=51+1+1+1+1+1

= 52•52•52 = 52+2+2 = 56

Power of Product

6. (ab)m = ambm

(3b)3 = (3•b)3

= (3•b)(3•b)(3•b)=3•3•3•b•b•b=31+1+1•b1+1+1

= 33•b3 = 27b3

7. a m = am , b0

b bm 2s 3

t= 2•2•2•s•s•s= 23s3

Power of Quotient

= (2s)(2s)(2s) t • t • t

t • t • t t3= 8s3

t3

Examples:

1. (2a2b3)3 =2. (p2 / q4)4 =

3. 32 m5 3 = 33m2

4. (43r4/ 44r6 )3 =

Examples:

5. c2d6 • 25c7 4 - 23c2d2

6. x5 y6•22x 3y5 3 - 25xy5• x2y3

7. h2k7• h5k2/ h7k3 =

Examples:

1. (q5 • r – 7 ) 3 =2. (w0 x– 3 • w3x3) 4 =

3. 32 s–3 5 - 34s–2

4. (5– 2k4 / 5–2k–6)2 =

Examples:

5. a–3b– 6 • a5b8 – 3 - a–2b2

6. t– 6 v0•2– 4t– 2v–4 2 - 2– 4 t0v– 3• t5v7

7.(c–4d–3• c–2d0/c–6d-3)4-