(-2ab^3)^4

2 min read Jun 16, 2024
(-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.

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