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Learn how to solve problems step by step online. Simplify the quotient of powers ((-5x^3y^2)^3(xy^5)^2)/((-5x^(-1)y)^(-1)). The power of a product is equal to the product of it's factors raised to the same power. When multiplying exponents with same base we can add the exponents. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify \left(\left(-5x^{-1}y\right)^{-1}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -1 and n equals 2.
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more