Solved Example > No. SE 10

How to find the value of x in a given expression using properties of exponents?

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Explanation:

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. (Our solved example in mathguru.com uses this concept)

Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q.

http://en.wikipedia.org/wiki/Rational_number

Exponentiation

Exponentiation is a mathematical operation, written as aⁿ, involving two numbers, the base a and the exponent (or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a (the product itself can also be called power)

$Description: a^n = \underbrace{a \times \cdots \times a}_n,$

just as multiplication by a positive integer corresponds to repeated addition

$Description: a \times n = \underbrace{a + \cdots + a}_n.$

Identities and properties

The most important identity satisfied by integer exponentiation is

$Description: a^{m + n} = a^m \cdot a^n$

(Our solved example in mathguru.com uses this concept)

This identity has the consequence

$Description: a^{m - n} =\frac{a^m}{a^n}$

for a ≠ 0, and

$Description: (a^m)^n = a^{m\cdot n}$

Another basic identity is

$Description: (a \cdot b)^n = a^n \cdot b^n$

http://en.wikipedia.org/wiki/Exponentiation

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.