%5E4.jpeg "(-2ab^3)^4")
Simplifying (-2ab^3)^4
This article will guide you through simplifying the expression (-2ab^3)^4.
Understanding Exponents
An exponent indicates how many times a base is multiplied by itself. In this case, the base is -2ab^3 and the exponent is 4.
Applying the Power of a Product Rule
The power of a product rule states that the power of a product is equal to the product of the powers of each factor. This rule applies to all factors within the parentheses.
Therefore, we can expand (-2ab^3)^4 as:
(-2ab^3)^4 = (-2)^4 * (a)^4 * (b^3)^4
Applying the Power of a Power Rule
The power of a power rule states that the power of a power is equal to the product of the exponents. This rule applies to the term (b^3)^4.
Expanding further:
(-2)^4 * (a)^4 * (b^3)^4 = 16 * a^4 * b^(3*4)
Simplifying the Expression
Finally, we simplify the expression:
16 * a^4 * b^(3*4) = 16a^4b^12
Conclusion
Therefore, the simplified form of (-2ab^3)^4 is 16a^4b^12. Remember to apply the appropriate exponent rules when simplifying expressions involving powers.