$$
\begin{aligned}
& \frac{\sqrt{x^{5}}}{\sqrt[3]{x^{4}}}=x^{\frac{a}{b}} \
& ext { If } \frac{\sqrt[3]{x^{4}}}{\sqrt[3]{x^{4}}}=x^{\frac{a}{b}} ext { for all positive values of } x \
& ext { what is the value of } \frac{a}{b} ext { ? }
\end{aligned}
$$

Question

$$
\begin{aligned}
& \frac{\sqrt{x^{5}}}{\sqrt[3]{x^{4}}}=x^{\frac{a}{b}} \
& 	ext { If } \frac{\sqrt[3]{x^{4}}}{\sqrt[3]{x^{4}}}=x^{\frac{a}{b}} 	ext { for all positive values of } x \
& 	ext { what is the value of } \frac{a}{b} 	ext { ? }
\end{aligned}
$$

StudyXY · Accepted Answer

: Identify the numerator and denominator of the given equation. : Simplify both the numerator and the denominator. : Set up the equation with the simplified numerator and denominator. : Use the rule of exponents to combine the base terms on both sides of the equation. : Set the exponents equal to each other since the base terms are equal. : Find a common denominator for the fractions on the right-hand side of the equation. : Multiply both the numerator and denominator of each fraction by the necessary factor to obtain the common denominator. : Solve for the ratio $$\frac{a}{b}$$. : Simplify the expression for the ratio. The value of the ratio $$\frac{a}{b}$$ is $$\frac{11}{3}$$.

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QuestionAnatomy and Physiology

Answer

Full Solution Locked

Step 1
: Identify the numerator and denominator of the given equation.

Step 2
: Simplify both the numerator and the denominator.

Final Answer

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