The laws of exponents simplify expressions when like terms have the same powers, but when a fraction has a negative or positive exponent, the simplified expression must be equal to the original one. The following table outlines the laws of expansion, decomposition, and divisors and how they relate to the process of simplifying expressions. To make use of this table, download Active Learning 1 and distribute the exponents to find a solution.
The laws of exponents simplify expressions that contain more than one operand. You can simplify any complex expression by combining the powers of the exponents in a single operation. For example, consider the example below. It shows an expression with two operands with two different powers. The product of two exponents gives the result of a single operation. If the product is a positive number, then it’s simplified by using the power rule.
In an interactive, students can explore the differences between these two methods. The table provides both the steps used to simplify an expression. In the first step, students should rewrite the negative exponents as positive. The second step involves applying the product rule to the exponents. This interactive provides the same solutions, but in a different order. Whichever method you use, you’ll have a much easier time tackling equations involving exponents.
For example, the two students’ answers are the same. In each case, they used different coefficients and exponents to simplify the expression. In the first case, Frankie got -4 and Marilyn got -64 using the product rule of exponents. However, the second solution is correct. In the second case, the two women used the same formula, but they couldn’t tell which one was right.
The laws of exponents are an essential part of mathematics education. These laws simplify complex mathematical expressions. They are the key to a student’s success. The laws of exponents are helpful in the context of a wide variety of applications. So, if you’re unsure of which way to apply the laws of exponotors, just check out the interactive below.
The laws of exponents allow you to simplify complex expressions without using a calculator. As you can see, there are different ways to use the laws of exponents to simplify an expression. It’s up to you to choose which method you prefer. You can even try both methods in the same context. For instance, if the equation has a fractional component, you’ll need to multiply the fraction by the same number in the opposite direction.