If a number is multiplied by itself a number of times, that number of times is indicated by the exponent. They are also called ‘power’. In mathematics, there are specific rules laid down to solve questions containing exponents. In algebra, we frequently use exponents in the expressions. One can multiply exponents the same way as we do multiplication for other numbers.
Using a few basic properties, exponents can often be simplified, since exponents represent repetitive multiplication. The fundamental structure of an exponent’s writing looks like x^y, where x is defined as the base and y is called its exponent. In this example, y is the number of times the variable x is multiplied by itself.
Suppose 2 is multiplied by 6 times, so it is written as 26, which is called as 2 to the power of 6, or 2 raised to the power of 6. Multiplication of exponents is a very useful operation, many times it is often not realized that whether one is dealing with stock market fluctuations or studying earthquakes to dealing with nuclear science, etc. all involve multiplication of exponents. We will be having a look at the multiplication of exponent rules below.
A very important aspect of algebra is multiplying exponents, it is the presence of exponents that make an algebraic expression as binomial or polynomial, etc. So it is very useful and important to understand how operations involving exponents are carried out. But before delving into the multiplication of exponents, it is of much importance to understand the basics of exponents themselves as to understand exponents fundamentally makes the operations of exponent much more easily understandable.Exponent like 24 is essentially 2 × 2 × 2 × 2 = 16.
Here the first number that is 2 in our example is the base and the second number 4 is the exponential. Multiplication of exponent can be done in five ways, let’s see them below :
- When the bases of two multiplying exponents are the same, we can add the powers and keep the base the same in the final answer. For example, let us have a look at the below examples wherein the base is the same for both the numbers only the exponent value is different.
- 24 × 22 = 24+ 2 = 26
- 32 × 33 = 32+3 = 35
- 42 × 43 = 42+3 = 45
- When multiplying two terms having coefficients and variables then multiply the coefficients together and then add the exponential value of the variable base.
- 4x5 × 3x2 = 12x5+3 = 12x8
- 3y2 × 2y = 6 y 2+1 = 6y3
- 10x2 × 2x10 = 20 x2+10 = 20x12
- When multiplying two terms with different bases but the same exponent value, then we can add the base values and keep the same exponent value in the final result. For example,
- 54 × 24 = 104
- 23 × 33 = 63
- 42 × 22 = 82
- When we have to multiply two terms that have both different bases and different exponents, then we don’t have any simplified trick as above to get the result, and to get the answer the exponent needs to be calculated completely. For example,
- 23 × 32 = 8 × 9 = 72
- 42 × 21 = 16 × 2 = 32
- 33 × 102 = 9 × 100 = 900
- When terms involved have negative exponent values, then the rules while are the same care has to be taken of the negative sign of the exponent when doing operations. Do note that a negative exponent indicates that the base is in fact a denomination of a fraction with a numerator as 1. So when multiplying the terms with negative exponents the below rules are else the same for example if their bases are the same add the exponents and multiplication of the bases if the exponents are the same and if nothing is the same then solve it directly.