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The power rule in algebra is a handy tool for dealing with expressions that contain exponents. It essentially states that when you have a term raised to a power, you can expand it by multiplying the base by itself as many times as the exponent indicates.

Take the expression \((-2y)^4\) as an example. The 4 in the exponent tells us to multiply \(-2y\) by itself four times. This means the expression becomes \((-2y) \times (-2y) \times (-2y) \times (-2y)\). Applying the power rule simplifies working with powers and helps to break down tasks into easier, repetitive multiplication steps.

Recognizing when and how to apply the power rule simplifies many algebraic procedures and helps with other complex algebra topics.

Exponents are a shorthand notation in mathematics to indicate repeated multiplication. An exponent consists of a base, which is the number being multiplied, and an exponent, which tells how many times the base is multiplied by itself.

For example, in the expression \((-2y)^4\), \(-2y\) is the base and 4 is the exponent. This indicates that \(-2y\) should be multiplied by itself four times.

• Base: This is the main number or variable that is repeatedly multiplied.
• Exponent: This is the small number written on the upper right-hand side that signifies how many times to multiply the base by itself.

Exponents make it easier to express large numbers or lengthy multiplications. Instead of writing out mulitple products, we can use exponents to convey the same information compactly and clearly.

Simplifying an expression is the process of reducing it to its simplest form while maintaining its original value. In algebra, this often involves removing exponents (turning them into expanded forms) and performing actual multiplications or distributions.

Returning to \((-2y)^4\), after expanding it to \((-2y) \times (-2y) \times (-2y) \times (-2y)\), we multiply the terms.

• First, multiply the numerical parts: \(-2 \times -2 \times -2 \times -2 = 16\).
• Next, handle the variable part: \(y \times y \times y \times y = y^4\).

This simplification process helps us rewrite complex expressions in a more manageable and insightful form, making them easier to understand and work with in subsequent calculations.