integer_exponents

# integer_exponents - Integer Exponents A real number raised...

This preview shows pages 1–4. Sign up to view the full content.

Integer Exponents A real number raised to a positive integer power . We start with a few examples involving powers of 7. = 7 2 7 x = 7 49 = 7 3 7 x 7 x = 7 49 x = 7 343 = 7 4 7 x 7 x 7 x = 7 343 x = 7 2401. In general, if a is a real number, and n is a positive integer, then = a n a . a . a . . . . a ------- (i) \_____________/ n times __________ The value of a n is obtained by multiplying a by itself n times. Here are some more examples. = ( ) - 3 4 ( ) - 3 . ( ) - 3 . ( ) - 3 . = ( ) - 3 81 = ( ) - 3 5 ( ) - 3 . ( ) - 3 . ( ) - 3 . ( ) - 3 . = ( ) - 3 - 243 = - 3 4 - ( ) 3 . 3 . 3 . 3 = - 81 = 3 2 3 3 2 . 3 2 . = 3 2 27 8 = - 2 5 6 - 2 5 . - 2 5 . - 2 5 . - 2 5 . - 2 5 . = - 2 5 ( ) - 2 6 5 6 = 2 6 5 6 = 64 15625 In general, we have the formula = a b n a n b n ------- (ii), ______ where a and b are real numbers with b 0, and n is a positive integer. For example, = π 2 4 π 4 16 = 2 3 4 2 . 2 . 2 . 2 3 4 = ( ) 2 . 2 . ( ) 2 . 2 3 4 = 2 . 2 3 4 = 4 81 . Similarly, = ( ) a b n a n b n ------- (iii), ______ where a and b are real numbers and n is a positive integer. For example, = ( ) 2 . 3 4 ( ) 2 . 3 . ( ) 2 . 3 . ( ) 2 . 3 . ( ) 2 . 3 = ( ) 2 . 2 . 2 . 2 . ( ) 3 . 3 . 3 . 3 = 2 4 . 3 4 = 16 x = 81 1296.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Evaluating the product 2 . 3 inside the bracket first gives the same result: ( ) 2 . 3 4 = = 6 4 1296. In general, = ( ) a b n ( ) a b x ( ) a b x . . . . x ( ) a b \_______________________/ n times = ( ) a . a . . . a x ( ) b . b . . . b \_________/ \_________/ n times n times = a n x b n . For example, = ( ) 2 π 4 2 4 . = π 4 16 π 4 . Also = ( ) 5 3 3 5 3 . = 3 3 125 . 3 . 3 . 3 = 125 . 3 . = 3 375 3 If m and n are positive integers, then a m . = a n a ( ) + m n ------- (iv) _______ For example, a 4 . a 3 = ( ) a . a . a . a x ( ) a . a . a = a . a . a . a . a . a . a = a 7 . In general, a m . = a n ( ) a . a . . . a x ( ) a . a . . . a \_________/ \_________/ m times n times = ( ) a . a . a . . . a \____________/ + m n times = a ( ) + m n . For example, 3 4 x = 3 2 3 6 = 729. If m > n and a 0, then = a m a n a ( ) - m n ------- (v). ______ For example, = a 5 a 3 a . a . a . a . a a . a . a = a . a . a a . a . a . a . a = 1 . a . a = a 2 .
In general, a m a n = a n . a ( ) - m n a n = a n a n . a ( ) - m n = 1 . a ( ) - m n = a ( ) - m n . For example, = 10 11 10 8 10 3 = 1000. If m < n and a 0, then = a m a n 1 a ( ) - n m ------- (vi). ______ For example,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/12/2011 for the course MATH 111 taught by Professor Uri during the Spring '08 term at Rutgers.

### Page1 / 10

integer_exponents - Integer Exponents A real number raised...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online