Exponent rules tutorial
Introduction :
A teaching process to a group of members is known as tutorial. Every concept should be clearly explained by tutorial. Exponent is a number which has a power in it. For example, 103 is an exponent where 10 is called as base and 3 is called as power. Exponent rules are the rules to be followed for doing problems in exponents.
Explanation to exponent rules tutorial:
Exponent rules are as follows.
Rule 1:
Multiplication:
Multiply Exponents gives the addition of its powers.
Example: ma × mb = ma+b
Rule 2:
Division:
Division of exponents gives the subtraction of powers.
Example: ma ÷ mb = ma-b
Rule 3:
If an exponent has more than one power, then multiply the powers to make it as a single power.
Example: (ma)b = mab
Some other rules of exponents are:
Example problems to exponent rules tutorial:
Example: 1
Simplify using exponent rule: 103 . 105 . 107
Solution:
Given: 103 . 105 . 107
103 . 105 . 107 = 103 + 5 + 7 (Rule 1)
= 1015
Answer: 103 . 105 . 107 = 1015
Example:
Simplify using exponent rule: `(8^5)/(8^6)`
Solution:
Given: `(8^5)/(8^6)`
`(8^5)/(8^6)` = 85-6 (Rule 2)
= 8-1
= `1/8^1`
Answer: `(8^5)/(8^6)``1/8`
Example: 3
Simplifying Exponents rule: `((7^2)^3)^2`
Solution:
Given exponent is `((7^2)^3)^2`
Step 1:
`((7^2)^3)^2` = `((7^2)^3)`.`((7^2)^3)`
Step 2:
`((7^2)^3)^2` = 72 × 3 . 72 × 3
= 76 76
= 66 + 6
= 712
or
`((7^2)^3)^2` 72 × 3 × 2 (Rule 3)
= 712
Example: 4
Simplify using exponent rule: 54 . 64 . 53 . 62
Solution:
Given: 54 . 64 . 53 . 62
54 . 64 . 53 . 62 = 54 . 53 . 64 . 62
= 54+7 . 64+2
= 511 . 610
Answer: 54 . 64 . 53 . 62 = 511 . 610
Practice problems to exponent rules tutorial:
Problem: 1
Simplify using exponent rule: 94 . 95
Answer: `1/9`
Problem: 2
Simplify using exponent rule: 116 ÷ 116
Answer: 1
Problem: 3
Simplify using exponent rule: `(6^5)^2`
Answer: 610
A teaching process to a group of members is known as tutorial. Every concept should be clearly explained by tutorial. Exponent is a number which has a power in it. For example, 103 is an exponent where 10 is called as base and 3 is called as power. Exponent rules are the rules to be followed for doing problems in exponents.
Explanation to exponent rules tutorial:
Exponent rules are as follows.
Rule 1:
Multiplication:
Multiply Exponents gives the addition of its powers.
Example: ma × mb = ma+b
Rule 2:
Division:
Division of exponents gives the subtraction of powers.
Example: ma ÷ mb = ma-b
Rule 3:
If an exponent has more than one power, then multiply the powers to make it as a single power.
Example: (ma)b = mab
Some other rules of exponents are:
- x-m =` 1/x^m`
- x0 = 1
Example problems to exponent rules tutorial:
Example: 1
Simplify using exponent rule: 103 . 105 . 107
Solution:
Given: 103 . 105 . 107
103 . 105 . 107 = 103 + 5 + 7 (Rule 1)
= 1015
Answer: 103 . 105 . 107 = 1015
Example:
Simplify using exponent rule: `(8^5)/(8^6)`
Solution:
Given: `(8^5)/(8^6)`
`(8^5)/(8^6)` = 85-6 (Rule 2)
= 8-1
= `1/8^1`
Answer: `(8^5)/(8^6)``1/8`
Example: 3
Simplifying Exponents rule: `((7^2)^3)^2`
Solution:
Given exponent is `((7^2)^3)^2`
Step 1:
`((7^2)^3)^2` = `((7^2)^3)`.`((7^2)^3)`
Step 2:
`((7^2)^3)^2` = 72 × 3 . 72 × 3
= 76 76
= 66 + 6
= 712
or
`((7^2)^3)^2` 72 × 3 × 2 (Rule 3)
= 712
Example: 4
Simplify using exponent rule: 54 . 64 . 53 . 62
Solution:
Given: 54 . 64 . 53 . 62
54 . 64 . 53 . 62 = 54 . 53 . 64 . 62
= 54+7 . 64+2
= 511 . 610
Answer: 54 . 64 . 53 . 62 = 511 . 610
Practice problems to exponent rules tutorial:
Problem: 1
Simplify using exponent rule: 94 . 95
Answer: `1/9`
Problem: 2
Simplify using exponent rule: 116 ÷ 116
Answer: 1
Problem: 3
Simplify using exponent rule: `(6^5)^2`
Answer: 610