# Exponential Form Meaning And Examples

The exponential form is a way of writing repeated multiplications of the same number multiplication involving base and exponents. The exponent can also be referred to as index or power. For example, 2 × 2 × 2 can be written as 2^{3} in the exponential form, where 2 is the base and 3 is the power.

The standard way of representing it is a^{b}, where a is the base and b is the order. When a number is represented in this form, the exponent represents the number of times the base will multiply itself.

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**How to Write a Number in Exponential Form**

Before I proceed to give some examples, there is an index law that states that any base number with the exponent of zero is 1. This means if “a” is any number and “b = 0” then the answer is 1 (2^{0} = 10^{0} = a^{0} = 9^{0} = 1)

### Exponential form of 64

Like I have stated above that exponents simply refer to the number of times a particular number appears in a numerical term.

64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^{6}

The base is 2 and the power is 6. This means 2 will multiply itself six times to give 64.

### Exponential form of 625

The first thing to do is to use prime factorization i.e. finding the smallest prime number that can divide the number completely without leaving a reminder then multiply all the prime factors that are the divisors. In the case of 625, you can start with 5 as the divisor.

5 | 625 |

5 | 125 |

5 | 25 |

5 | 5 |

1 |

625 = 5 x 5 x 5 x 5 = 5^{4}

Therefore, the exponential form of 625 is 5^{4}

### Exponential form of 125

125 is when 5 multiplies itself three times

125 = 5 x 5 x 5 = 5^{3}

Therefore, the exponential form of 125 is 5^{3}

### Exponential form of 243

We can also look for prime factors of 243 and multiply them together and then express them in the exponent.

243 = 3 x 3 x 3 x 3 x 3 = 3^{5}

Therefore, the exponential form of 243 is 3^{5}