Exponentiation should be the operation, which is written as the form of an. Where a and n is said to be base and exponent as well as n is any positive integer. In general, exponentiation means that repetitive multiplication. Otherwise, exponentiation an is the product of n factors of a. Online study should be the topic-oriented or else technical help for clarifying doubts that are convey through the computer software. Let us study properties and example problems for exponentiation.
Properties - Study Online Exponentiation
We are having seven number of exponentiation properties that used for solving problems. In this properties, a, m and n are any integer values.
Product of like bases:
The product of powers with the same base means we can add the powers and keep the common base.
am an = am+n
Quotient of like bases:
To divide the powers with similar base, we can subtract the exponents and remain the common base.
`a^m/a^n` = am-n
Power to a power:
In case of raising the power to power, we need to keep same base and multiply the exponent values.
`(a^m)^(n)` = amn
Product to a power:
In case of raising the product to power, we need to raise each factor to the power value.
(ab)m = am bm
Quotient to a power:
In case of raising the quotient to power, we need to raise the numerator and denominator to the power value.
`(a/b)^n` = `a^n/b^n`
Zero exponent:
Any number that is raised with zero power should be equivalent to ‘1’.
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 online.
Example Problems - Study Online Exponentiation
Example 1:
Solve 32 34.
Solution:
Given, 32 34.
This is in the structure of am an, so we need to use am an = am+n property.
Here, m = 2 and n = 4 and a = 3.
Thus, 32 34 = 32+4
= 36
= 3 × 3 × 3 × 3 × 3 × 3
= 9 × 9 × 9
= 729
Hence, the answer is 32 34 = 729.
Example 2:
Shorten the following `6^7/6^4` .
Solution:
Given, `6^7/6^4` .
This is in the structure of `a^m/a^n` , so we need to use `a^m/a^n` = am-n property.
Here, m = 7 and n = 4 and a = 6.
Thus, `6^7/6^4` = 67-3
= 64
= 6 × 6 × 6 × 6
= 36 × 36
= 1296
Hence, the answer is `6^7/6^4` = 1296.
That’s all about the study online exponentiation.
Properties - Study Online Exponentiation
We are having seven number of exponentiation properties that used for solving problems. In this properties, a, m and n are any integer values.
Product of like bases:
The product of powers with the same base means we can add the powers and keep the common base.
am an = am+n
Quotient of like bases:
To divide the powers with similar base, we can subtract the exponents and remain the common base.
`a^m/a^n` = am-n
Power to a power:
In case of raising the power to power, we need to keep same base and multiply the exponent values.
`(a^m)^(n)` = amn
Product to a power:
In case of raising the product to power, we need to raise each factor to the power value.
(ab)m = am bm
Quotient to a power:
In case of raising the quotient to power, we need to raise the numerator and denominator to the power value.
`(a/b)^n` = `a^n/b^n`
Zero exponent:
Any number that is raised with zero power should be equivalent to ‘1’.
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 online.
Example Problems - Study Online Exponentiation
Example 1:
Solve 32 34.
Solution:
Given, 32 34.
This is in the structure of am an, so we need to use am an = am+n property.
Here, m = 2 and n = 4 and a = 3.
Thus, 32 34 = 32+4
= 36
= 3 × 3 × 3 × 3 × 3 × 3
= 9 × 9 × 9
= 729
Hence, the answer is 32 34 = 729.
Example 2:
Shorten the following `6^7/6^4` .
Solution:
Given, `6^7/6^4` .
This is in the structure of `a^m/a^n` , so we need to use `a^m/a^n` = am-n property.
Here, m = 7 and n = 4 and a = 6.
Thus, `6^7/6^4` = 67-3
= 64
= 6 × 6 × 6 × 6
= 36 × 36
= 1296
Hence, the answer is `6^7/6^4` = 1296.
That’s all about the study online exponentiation.
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