%5E4.jpeg "(-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.