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How do I add numbers raised to a power?

Published in Adding Exponents 2 mins read

To accurately answer the question "How do I add numbers raised to a power?", it's essential to understand that you can only directly add terms that have the same base raised to the same power. This is demonstrated in the reference YouTube video, which focuses on adding and subtracting expressions with exponents.

Here's a breakdown:

Adding Like Terms with Exponents

The key concept is identifying "like terms." Like terms are terms that have the same variable (base) raised to the same exponent.

  • Identify Like Terms: Look for terms where the base (usually a variable) and the exponent are identical. For example, 5x² and -3x² are like terms because they both have 'x' raised to the power of 2.
  • Combine Coefficients: Once you've identified like terms, add or subtract their coefficients (the numbers in front of the variable). Keep the base and exponent the same.

Examples:

  • 3x² + 2x² = 5x² (Both terms have x², so you add the coefficients: 3 + 2 = 5)
  • -4x³ + 7x³ = 3x³ (Both terms have x³, so you add the coefficients: -4 + 7 = 3) This example is explicitly provided in the reference material.

What if the bases or exponents are different?

If the terms do not have the same base and exponent, you cannot directly combine them. For instance:

  • x² + x³ cannot be simplified further because the exponents are different.
  • x² + y² cannot be simplified because the bases are different.

In these cases, you would leave the expression as is, unless you can simplify individual terms through other mathematical operations (like factoring).

Special Cases and Considerations

  • Constants: Constants (numbers without variables) can be added together. For example, 5 + 3 = 8. The reference gives the example of "+ 5" being on its own.
  • Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. Exponents are evaluated before addition or subtraction.
  • Negative Exponents: Make sure to correctly handle negative exponents. For example, x-1 = 1/x

Summary Table

Expression Like Terms? Simplified Result
4x² + 5x² Yes 9x²
2x³ - x³ Yes x³
7y² + 3y No 7y² + 3y
5 + 2 Yes 7
-2x² + 5 + 8x² Yes 6x² + 5

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