(-2a)^4

2 min read Jun 16, 2024
(-2a)^4

Simplifying (-2a)^4

This expression involves raising a binomial with a negative coefficient to the fourth power. Let's break down how to simplify it step-by-step.

Understanding the Exponent

The exponent 4 tells us to multiply the base, (-2a), by itself four times:

(-2a)^4 = (-2a) * (-2a) * (-2a) * (-2a)

Applying the Rules of Exponents

  • Product of Powers: When multiplying exponents with the same base, we add their powers. In this case, we have (-2)^4 and (a)^4.
  • Even Exponent: An even exponent applied to a negative number results in a positive number.

Simplifying the Expression

Following these rules, we can simplify the expression:

  • (-2)^4 = 16 (since -2 * -2 * -2 * -2 = 16)
  • (a)^4 = a^4

Therefore, the simplified expression is:

(-2a)^4 = 16a^4

Key Points to Remember

  • Parentheses are important: In expressions like this, the parentheses indicate that the entire binomial (-2a) is being raised to the fourth power.
  • Apply exponents to both terms: The exponent 4 applies to both the coefficient (-2) and the variable (a).
  • Even exponents and negative signs: Even exponents on negative numbers result in positive numbers.

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