Exponents Formula
The exponent of a number shows how many times the 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?
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 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.

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}.