Exponents and powers are a method to express repeated multiplication of the same number. For eg- 6×6×6×6 can be written as 64 where 6 is the base and 4 is the exponent. It is most commonly used to express the powers of 10 to write a very large number in a convenient manner. For eg- 100000 can be written as 105.
Laws of Exponents
- To multiply two exponential numbers with the same bases, the exponents are added and the base remains the same. For eg- am × an = am+n
- When the exponent has another exponent, the base remains the same but the powers are multiplied.
For eg- (am)n = am×n
- To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same.
For eg- am/an = am-n
What is a Power Notation?
Power notation is a method to express numbers that are very large or very small. For eg- 10000000000000 can be written as 1013 and 0.000000016 can be written as 1.6 × 10-8
Steps to write a number in the power notation:
Step 1: Write the number and do its factorization.
Step 2: Count the number of times the factor is there.
Step 3: Write the exponential number with the number as the base and the number of times it appeared as the power.
What is 125 in the exponential form?
Given that the number is 125.
The factors of 125 are 125 = 5 × 5 × 5
The factors appeared for 3 times.
125 = 53
Hence, the power notation of 125 is 53.
Question 1: What is the power notation of 32?
Given that the number is 32.
The factors of 32 are 32 = 2 × 2 × 2 × 2 × 2
The factors appeared for 5 times.
32 = 25
Hence, the power notation of 32 is 25.
Question 2: What is the power notation of 216?
Given that the number is 216.
The factors of 216 are 216 = 2 × 2 × 2 × 3 × 3 × 3 = 6 × 6 × 6
The factor appeared for 3 times.
216 = 63
Hence, the power notation of 216 is 63.
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