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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\frac{dy}{dx}y=\frac{\sqrt{\left(x+3\right)^8}}{\sqrt{\left(4x-5\right)^{10}}}$
Learn how to solve problems step by step online. Solve the differential equation dy/dxy=(((x+3)^8)/((4x-5)^10))^(1/2). The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Simplify \sqrt{\left(x+3\right)^8} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 8 and n equals \frac{1}{2}. Simplify \sqrt{\left(4x-5\right)^{10}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 10 and n equals \frac{1}{2}. Multiply the fraction and term in 8\cdot \left(\frac{1}{2}\right).
