Exponent Rules: Understanding Bases and Exponents, Summaries of Elementary Mathematics

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Exponent Rules

Parts  When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.

n

b

The Invisible Exponent  When an expression does not have a visible exponent its exponent is understood to be 1.

1 x  x

Exponent Rule #  When same base you multiplying add two expressions with thetheir exponents.

 For example

b n^  b m  b n  m

x^2  x^4 ^ x^2 ^4 ^ x^6 2  22  2 1  (^22)  2 1 ^2  (^23)  8

Exponent Rule #  When raising a multiply the exponents power to a power you

 For example

( b n ) m  b n  m

( x^2 )^4  x^2 ^4  x^8 ( 22 )^2  2 2 ^2  24 ^16

Exponent Rule #

 Try it on your own

( b n ) m  b n  m

5. ( h^3 )^2  h^3 ^2  h^6
6. ( 32 )^2  3 2 ^2  34  81

Exponent Rule #  When a product is raised to a power, each piece is raised to the power

 For example

( ab ) m  a m^ b m ( xy )^2  x^2 y^2 ( 2  5 )^2 ^2 2 ^52 ^4 ^25 ^100

Exponent Rule #  Try it on your own

( ab ) m  a m^ b m

7. ( hk )^3  h^3 k^3

8. ( 2  3 )^2  2 2  (^32)  4  9  36

Exponent Rule #6:  When anything, except 0, is raised to the zero^ Zero Exponent power it is 1.

 For example

a^0  1 ( if a^ ≠ 0)

x^0 ^1 ( if x^ ≠ 0)

Zero Exponent

 Try it on your own

a^0  1 ( if a^ ≠ 0)

11. h^0  1 ( if h^ ≠ 0)

13. 0 0  undefined