Question

Write the laws of exponent, if x, y are positive real numbers and m, n are rational numbers. ​

Answer 1

Supposed you are asked to calculate or multiply large numbers and you don’t have an electronic calculator. What if you get the wrong answer? How can we make this calculation easier? So let us try to understand some of the exponent rules for real numbers.

Laws of Exponents or Exponent Rules

What is meant by an exponent? You must have come across the expression 3². Here 3 is the base and 2 is the exponent. Exponents are also called Powers or Indices. The exponent of a number tells how many times to use the number in a multiplication. Let us study the laws of exponent. It is very important to understand how the laws of exponents laws are formulated.

Exponent Rules

(Source: math warehouse)

1. Product law

According to the product law of exponents when multiplying two numbers that have the same base then we can add the exponents

am × an= a m+n

where a, m and n all are natural numbers. Here the base should be the same in both the quantities. For example,

2³ × 24 = 27
22/3 × 21/5 = 2 2/3 + 1/5 = 2(10+3)/15 . We get, = 212/15
(-6) 3 x (-6) 2 = (-6) 3+2 = (-6) 5

Answer 2

Answer:

As x and y are positive real numbers then we can write

By using law of rational exponents we have

Hence the simplified value of is