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Understanding the rule of exponents is a foundational skill in algebra that helps deal with operations involving powers. The given exercise \(\left(\frac{-2 a}{b}\right)^{5}\) requires applying this rule for simplification.

When an entire fraction is raised to an exponent, both the numerator and the denominator of the fraction are raised to that power separately. This means that you perform the exponentiation on the top number (numerator) and the bottom number (denominator) independently. Given this rule, \(\left(\frac{-2a}{b}\right)^5\) simplifies to \(\frac{(-2a)^5}{b^5}\), which is exactly what is done in Step 1 of the solution.

Remember, when an expression that includes a negative number is raised to an odd power, the result is negative, which is crucial for correctly solving such problems.

Numerical simplification involves reducing expressions to their simplest form while preserving their values. Focusing on the numerator in Step 2, \( (-2)^5 \), the process involves multiplying \( -2 \) by itself five times: \( -2 \times -2 \times -2 \times -2 \times -2 \), which equals \( -32 \).

For variables with exponents, the power indicates how many times the variable is multiplied by itself. Therefore, \( a^5 \) means \( a \times a \times a \times a \times a \). Combining the numerical and variable parts, the expression simplifies to \( -32a^5 \), ensuring a thorough numerical simplification as achieved in the second step of the provided solution.

Algebraic fractions are fractions that contain algebraic expressions in the numerator, denominator, or both. These may seem intimidating at first, but simplifying algebraic fractions follows the same principles as simplifying numerical fractions.

Consider the final form \( -32a^5 / b^5 \), obtained in Step 3 from the original exercise. The approach was straightforward here because there was no additional simplification needed. However, managing more complex algebraic fractions generally requires factoring the numerator and denominator, reducing common factors, and applying rules of exponents where necessary.

Understanding how to deal with exponents in algebraic fractions is vital for simplifying expressions and solving equations that build upon this concept. Always keep an eye out for opportunities to reduce and simplify terms in order to achieve the most simplified version of an expression.