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Add and Subtract Terms with Negative Exponents Calculator

Reviewed by Calculator Editorial Team

This guide explains how to add and subtract terms with negative exponents, including the rules for combining like terms and simplifying expressions. The calculator helps you perform these operations quickly and accurately.

How to Use This Calculator

To use the calculator:

  1. Enter the first term in the format a * x^b where a is the coefficient, x is the variable, and b is the exponent.
  2. Enter the second term in the same format.
  3. Select whether you want to add or subtract the terms.
  4. Click "Calculate" to see the result.
  5. Click "Reset" to clear the inputs.

The calculator will show you the simplified result and explain how it was obtained.

Formula Explained

When adding or subtracting terms with negative exponents, follow these rules:

For terms with the same variable and exponent:

Addition: a * x^b + c * x^b = (a + c) * x^b

Subtraction: a * x^b - c * x^b = (a - c) * x^b

If the exponents are different, the terms cannot be combined. For example, x^-2 and x^-3 are not like terms and cannot be added or subtracted directly.

Worked Examples

Example 1: Adding Terms

Add 3x^-2 + 5x^-2:

  1. Identify the coefficients: 3 and 5.
  2. Add the coefficients: 3 + 5 = 8.
  3. Keep the same exponent: x^-2.
  4. Result: 8x^-2.

Example 2: Subtracting Terms

Subtract 7x^-3 - 2x^-3:

  1. Identify the coefficients: 7 and 2.
  2. Subtract the coefficients: 7 - 2 = 5.
  3. Keep the same exponent: x^-3.
  4. Result: 5x^-3.

Common Mistakes

When working with negative exponents, common mistakes include:

  • Adding or subtracting terms with different exponents.
  • Forgetting to combine the coefficients when the exponents are the same.
  • Incorrectly simplifying the result after performing the operation.

Always ensure the exponents are the same before adding or subtracting terms. If they are different, the terms cannot be combined.

FAQ

Can I add terms with different negative exponents?

No, terms with different exponents cannot be added or subtracted directly. They must be simplified or rewritten with the same exponent before combining.

What happens if I subtract a larger term from a smaller one?

The result will be a negative term with the same exponent. For example, 2x^-3 - 5x^-3 = -3x^-3.

Can I use this calculator for positive exponents?

Yes, the calculator works for both positive and negative exponents as long as the exponents are the same when adding or subtracting.