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Simplifying algebraic expressions is an essential skill that allows you to express an equation or an expression in its most basic and understandable form. To simplify an expression, follow the established hierarchy of operations: deal with parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).In our textbook example, \(\left(\frac{-2 x y^{4}}{z^{3}}\right)^{5}\), we simplify by first addressing the exponents within the parentheses, utilizing the exponent multiplication rule we've already discussed. Next, we simplify the numerical coefficient \(\left(-2\right)^{5}= -32\) as a separate entity. Finally, we rewrite the terms with their new exponents to get \(\frac{-32x^5y^{20}}{z^{15}}\), which is a clear, straightforward version of our original complex expression.
Simplifying an expression can often reveal properties of the equation and make it easier to work on subsequent calculations or to understand the relationship between the variables. Repetitive practice in simplifying algebraic expressions enhances problem-solving skills and mathematical comprehension.