# Exponents Formula

The exponent of a number refers to the number of times any number is multiplied by itself. There are various exponents formulas used to solve the equations. Exponents are important because they help in representing products where a number is repeated by itself many times. Let's learn about exponents formulas with a few solved examples in the end.

## What Are the Exponents Formulas?

Exponents formulas refer to the formulas that help solve exponents. Exponent of a number is represented in the form: x^{n}, meaning x is multiplied by itself for n times.^{ }Here,

- x is called the "base"
- n is called the "exponent" or "power"
- x
^{n}is read as "x to the power of n" (or) "x raised to n"

### Exponents Formulas

Exponents formulas are expressed as:

- a
^{0 }= 1 - a
^{1}= a - a
^{m }× a^{n }= a^{m+n} - a
^{m }/ a^{n }= a^{m−n} - a
^{−m }= 1/a^{m } - (a
^{m})^{n }= a^{mn} - (ab)
^{m }= a^{m}b^{m} - (a/b)
^{m }= a^{m}/b^{m}

Let us understand exponents formulas better using a few solved examples.

## Examples Using Exponents Formulas

**Example 1: **In a forest, each tree has about 5^{7} leaves and there are about 5^{3} trees in the forest. Using the exponents' formula, find the total number of leaves.

**Solution: **

To find: Total number of leaves.

The number of trees in the forest = 5^{3}

The number of leaves in each tree = 5^{7}(given)

Using the exponents formula,

a^{x} x a^{y} = a^{x+y}

Putting the values,

5^{3} x 5^{7} = 5^{3+7}

5^{3} x 5^{7} = 5^{10}

**Answer: The total number of leaves is 5 ^{10}.**

**Example 2:** The dimensions of a wardrobe are x^{5} in, y^{3} in, and x^{8} in. Find its volume.

**Solution: **

To find: volume of the wardrobe.

The dimensions of the wardrobe are: length(l) = x^{5} in, width(w) = y^{3} in, height(h) = x^{8} in (given)

Using the exponents formula,

a^{x} x a^{y} = a^{x+y}

Putting the values,

Volume = x^{5} × x^{8 }× y^{3} = x^{13 }× y^{3}

Volume = x^{13 }× y^{3}

**Answer: The volume of the wardrobe is x ^{13} × y^{3}.**

**Example 3: **Determine the value of x^{-5/2} when x = 3.

**Solution: **

To find: the value of x^{-5/2}

Given: x = 3

Using the exponents formula,

x^{-5/2 }= (3)^{-5/2}

= (1/3)^{5/2}

= (1/3 × 1/3 × 1/3 × 1/3 × 1/3)^{1/2}

= (1/243)^{1/2}

= √(1/243) = 1/9√3.

**Answer: The value of x ^{-5/2} when x = 3 is 1/9√3.**

## FAQs on Exponents Formulas

### What Are Exponents Formulas in Math?

We know that the exponent of a number is represented in the form: x^{n} (n is the exponent). In other words, you can say that exponents are superscript numerals. Exponents formulas are the formulas that help solve problems that involve exponents. Some important exponents formulas are given as,

- a
^{0 }= 1 - a
^{1}= a - a
^{m }× a^{n }= a^{m+n} - a
^{m }/ a^{n }= a^{m−n} - a
^{−m }= 1/a^{m } - (a
^{m})^{n }= a^{mn} - (ab)
^{m }= a^{m}b^{m} - (a/b)
^{m }= a^{m}/b^{m}

### What Are the Applications of Exponents Formulas?

Exponents formulas have a wide range of applications:

- scientific scales like the pH scale or the Richter scale.
- calculating the area, volume, and other such problems.
- abbreviates something that would otherwise be really tedious to write.
- used in computer games, measuring scales.
- Science, Engineering, Economics, Accounting, Finance.
- Exponents are often used to describe a computer's memory.
- Making medicines in the laboratory.

### How To Use Exponents Formulas?

Exponent formulas are easy to use

- Step 1: Check for the given parameters.
- Step 2: Identify the suitable exponent formula.
- Step 3: Put the given values(base and power) in the formula.

### What Are the Components of the Exponent Formulas?

The exponent formulas include the bases and the powers and the mathematical symbols. Exponent of a number is represented as, x^{n}, where 'x' is base and 'n' is the power.