Study Exponentiation

In math, exponentiation is the operation, which is written as the form of an. Where a and n is said to be base and exponent and n is any positive integer. Normally, exponentiation means that repeated multiplication. Otherwise, exponentiation an is the product of n factors of a. The exponent is usually placed as a superscript to right of base value. We are having many properties for exponentiation. Let see properties and example problems for exponentiation.


Properties - Study Exponentiation


We are having seven number of exponentiation properties that used for solving problems with exponentiation. In this properties, a, m and n are any integer values.

Product of like bases:

am an = am+n

Quotient of like bases:

`a^(m)/a^(n)` = am-n

Power to a power:

` (a^(m))^(n)` = amn

Product to a power:

(ab)m = am bm

Quotient to a power:

`(a/b)^(n)` = `a^(n)/b^(n)`

Zero exponent:

a0 = 1

Negative exponent:

a-n = `1/a^(n)` or `1/a^(-n)` = an

These are the properties that are used for exponentiation problems in study math.


Example Problems - Study Exponentiation


Example 1:

Solve 23 22.

Solution:

Given, 23 22.

This is in the form of am an, so we need to use am an = am+n property.

Here, m = 3 and n = 2 and a = 2.

Thus, 23 22 = 23+2

= 25

= 2 × 2 × 2 × 2 × 2

= 32
Hence, the answer is 23 22 = 32.

Example 2:

Shorten the following `5^5/5^3`.

Solution:

Given, `5^5/5^3` .

This is in the form of `a^m/a^n` , so we need to use `a^m/a^n` = am-n property.

Here, m = 5 and n = 3 and a = 5.

Thus, `5^5/5^3` = 55-3

= 52

= 5 × 5

= 25
Hence, the answer is `5^5/5^3` = 25.

That’s all about the study exponentiation.