How to Multiply Exponents

How to Multiply Exponents

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So, when considering exponents in mathematics, they are basically defined as a number multiplied by itself certain number of times. For example, let’s see the number \(5^7\). Now, here we can clearly see that \(5\) is multiplied by itself \(7\) times. So, this will evaluate to \(5 \ \times \ 5 \ \times \ 5 \ \times \ 5 \ \times \ 5 \ \times \ 5 \ \times \ 5\). Hence, it's clearly evident, why we need to use exponents. This clearly saves time and looks neat when written in some algebraic expression or mathematical equation.
Now, let’s consider the same exponent \(5^7\). Here we can say that this exponent has 2 parts. In this case, \(5\) is referred to as the "base," while \(7\) is referred to as the "exponent" or "power." In the term \(x^n\):

• \(n\) is the exponent or power.
• \(x\) is called the base.

Properties of Exponents

When dealing with exponents, it is necessary to apply the properties of exponents or the rules of exponents in order to solve the problem. These characteristics are also referred to as major exponents rules, which must be observed when solving exponent problems. The next section discusses the properties of exponents.

• The Product Law states that \(a^m \times a^n \ = \ a^{m \ + \ n}\)
• The Law of Quotients states that \(\frac{a^m}{a^n} \ = \ a^{m \ - \ n}\)
• The Law of the Zero Exponent is as follows: \(a^0 \ = \ 1\)
• The Law of the Negative Exponent states that \(a^{-m} \ = \ \frac{1}{a^m}\)
• The Law of the Power of a Power is as follows: \((a^m)^n \ = \ a^{m \times n}\)
• The Power of a Product is defined as \((ab)^m \ = \ a^m \times b^m\)
• The Power of a Quotient is defined as \((\frac{a}{b})^m \ = \ \frac{a^m}{b^m}\)

Multiplication Properties of Exponents

Some properties of exponents multiplication are:

• The Product Law states that \(a^m \times a^n \ = \ a^{m \ + \ n}\)
• The Law of Quotients states that \(\frac{a^m}{a^n} \ = \ a^{m \ - \ n}\)
• The Law of the Power of a Power is as follows: \((a^m)^n \ = \ a^{m \times n}\)
• The Power of a Product is defined as \((ab)^m \ = \ a^m \times b^m\)

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