Mathguru – Help – To find the given expression using laws of exponents.

12.1 Introduction > No. 6(i)

To find the given expression using laws of exponents.

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Explanation:

Exponentiation

Exponentiation is a mathematical operation, written as aⁿ, involving two numbers, the base a and the exponent n. When n is a positive integer exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a:

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

Just as multiplication by a positive integer corresponds to repeated addition

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

The exponent is usually shown as a superscript to the right of the base. The exponentiation aⁿ can be read as: a raised to the n-th power, a raised to the power [of] n, or possibly a raised to the exponent [of] n, or more briefly as a to the n. Some exponents have their own pronunciation: for example, a² is usually read as a squared and a³ as a cubed.

Negative integer exponents

By definition, raising a nonzero number to the −1 power produces its reciprocal:

$Description: a^{-1} = \frac{1}{a}.$

One also defines

$Description: a^{-n} = \frac{1}{a^n}$

for any nonzero a and any positive integer n. (Our solved example in mathguru.com uses this concept)

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.