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Exponent Rules: 5 Key Strategies to Solve Tough Equations


Exponent rules explain the ways to simplify various equations with different types of exponents. Equations that contain exponents with the same base can be solved quickly, whereas, in the case of other equations, it is required to use logs to solve them. There are different kinds of exponent equations based on positive exponent, negative exponents, and rational exponent, which may look intimidating at first. However, with various learning strategies, you can make exponent rules easy to follow.

Before going to the strategies, let’s have a brief idea about what are exponents and their rules:

What are Exponents?

Exponents are also known as powers. It is a value that shows how many times a base number will multiply by itself. The number raised by power is known as the base, while the superscript number above it is the exponent or power. Types of exponents are

positive exponents, negative exponents, zero exponents, and rational exponents.

Exponent Rules

There are seven exponent rules, or laws of exponents, that apply to these exponents equations, and every student needs to learn them. Each rule shows how to solve different types of math equations and add, subtract, multiply and divide exponents. These seven exponent rules are:

  • Product of powers rule: If multiplying two bases with the same value, write the base same and then add the exponents to get the solution.
  • Quotient of powers rule: When dividing two bases of the same value, keep the base the same and subtract the exponent values.
  • When dividing exponent expressions with the same bases, just subtract the exponent’s power, keeping the same base.
  • Power of a power rule: This rule is used to solve exponent equations where one exponent power is raised by another power. In such equations, multiply the exponents together by keeping the same base.
  • Power of a product rule: When any base is being multiplied by an exponent, distribute the exponent to each part of the base.
  • Power of a quotient rule: This rule is about raising a quotient by a power. In this rule, the exponent needs to be distributed to all values of a quotient within the brackets.
  • Zero power rule: Any base raised to the power of zero is equal to one.
  • Negative exponent rule: When a number has a negative exponent, flip it into a reciprocal to turn the exponent into a positive exponent.

5 Key Strategies to Solve Tough Equations

1. Isolate the Exponential Expression by Keeping them on One Side of the Equation:

Make sure that there is an exponential expression on one side of the equation and a whole number on the other side. You need to rearrange the equation if it is not to keep the exponent on one side of the equation.

2. Check if any Two Exponents have the Same Base

If the base number is the same in an exponential expression, you can easily solve that equation by placing the exponent on either side.

3. Determine Whether any Two Exponents can be Canceled

While simplifying the exponent equations, check if there are terms that can be reduced or canceled. It will help in reducing the complexity of the equation.

4. Apply the Same Rule on Both Sides

While solving any exponent equation, remember to apply the same rules on both sides of the equation. If you perform some operation on one side of an equation, you must do it to the other side of the equation. For example, get the logarithms of both sides of the equation. You can use any bases for logs.

5. Factor the Terms to Yield Common Terms

Look for terms that can be factored in to yield a common term or solution.


Rote learning of various mathematical concepts leads to poor subject knowledge and lack of fundamental understanding to learn advanced concepts. This is a major cause of kids lacking interest in math. When kids learn math through active learning, reasoning, and logic, they gain the conceptual fluency required to form a solid math foundation. Cuemath encourages kids to learn math logically by strengthening their reasoning skills. Deep knowledge of each topic enables kids to form links and understanding through various math topics.

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