give reasons of solving rational exponent or radicals in terms of, addition, subtraction, multiplication and division.
Solving rational exponents or radicals involves working with powers and roots of numbers. Here are the reasons for solving rational exponents or radicals in terms of addition, subtraction, multiplication, and division:
1. Addition: Rational exponents and radicals can be added by combining their like terms. For example, if you have expressions with the same base and different exponents, you can add or subtract the exponents to simplify the expression. This is similar to how you would add or subtract variables with the same base.
2. Subtraction: Similar to addition, when you have rational exponents or radicals with the same base, you can subtract the exponents to simplify the expression. By subtracting one exponent from another, you can simplify and evaluate the expression.
3. Multiplication: Rational exponents and radicals can be multiplied by combining their bases and adding their exponents. In the case of multiplication, you can multiply the bases together and add their exponents, resulting in a simplified expression. Similarly, when multiplying radicals, you can multiply the numbers inside the radicals and simplify.
4. Division: When dividing rational exponents, you subtract the exponents of the same base. Division of radicals is similar, as you divide the numbers inside the radicals and simplify. Dividing rational exponents or radicals helps to simplify the expressions and solve them more efficiently.
In summary, rational exponents and radicals can be solved using addition, subtraction, multiplication, and division to simplify the expressions and make them easier to work with. These operations allow you to combine like terms, manipulate the exponents, and evaluate the expressions effectively.