# Powers

### Powers with an Integer Exponent  ### Powers with a Fractional Exponent  ### Properties

1, a0 = 1

2 a1 = a

3. Multiplication of powers with the same base:

It is another power with the same base and whose exponent is the sum of the exponents.

am · a n = am+n

(−2)5 · (−2)2 = (−2)5+2 = (−2)7 = −128

4. Division of powers with the same base:

It is another power with the same base and the exponent is the difference between the exponents.

am : a n = am — n

(−2)5 : (−2)2 = (−2)5 — 2 = (−2)3 = −8

5. Power of a power:

It is another power with the same base and the exponent is the product of the exponents.

(am)n = am · n

[(−2)3]2 = (−2)6 = 64

6. Multiplication of powers with the same exponent:

It is another power with the same exponent, whose base is the product of the bases

an · b n = (a · b) n

(−2)3 · (3)3 = (−6)3 = −216

7. Division of powers with the same exponent :

It is another power with the same exponent, whose base is the quotient of the bases.

an : b n = (a : b) n

(−6)3 : 33 = (−2)3 = −8