What is 125 in the exponential form?

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- a^m × aⁿ = a^m+n
• When the exponent has another exponent, the base remains the same but the powers are multiplied. 
  For eg- (a^m)ⁿ = a^m×n
• To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same. 
  For eg- a^m/aⁿ = a^m-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?

Solution:

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.

Similar Questions

Question 1: What is the power notation of 32?

Solution:

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?

Solution:

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.