Question

Perform the indicated operation. $$\left(-3 y^{3}\right)^{2}$$

   Perform the indicated operation.
$$\left(-3 y^{3}\right)^{2}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 5, Problem 77

Instant Answer

Solved by Expert Angela Guo

03/06/2020

Step 1

This means we have to square both the coefficient and the variable part. Show more…

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Perform the indicated operation. $$\left(-3 y^{3}\right)^{2}$$

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Key Concepts

Exponent Rules

The exponent rules encompass the properties used to simplify expressions involving powers. For example, when raising a power to another power, the exponents are multiplied. This rule is essential for simplifying expressions where an exponent is applied to a term that already has an exponent.

Power of a Product Rule

The power of a product rule states that when a product of factors is raised to an exponent, each factor is raised to that exponent independently. This means that (ab)^n can be rewritten as a^n multiplied by b^n, which simplifies the process of evaluating the expression.

Sign and Squaring Considerations

Squaring a number, whether positive or negative, always results in a positive value because multiplying two negative numbers yields a positive product. This aspect is important because it ensures the correct evaluation of the sign when an entire expression with a negative coefficient is squared.

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