How do you simplify $\frac{9 x^{4}}{35 y^{4}} \cdot \frac{15 x y}{3 x^{4} y^{2}}$ $\frac { 9x ^ { 4} } { 35y ^ { 4} } \cdot \frac { 15x y } { 3x ^ { 4} y ^ { 2} }$ ?

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How do you simplify $\frac{9 x^{4}}{35 y^{4}} \cdot \frac{15 x y}{3 x^{4} y^{2}}$ $\frac { 9x ^ { 4} } { 35y ^ { 4} } \cdot \frac { 15x y } { 3x ^ { 4} y ^ { 2} }$ ?

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Answer 1 · 2017-11-26T22:07:14

$\frac{9 x}{7 y^{5}}$ $(9x)/(7y^5)$

Explanation:

Instead of multiplying than simplifying, we could simplify the fractions, than cross-simplify.

Since $\frac{9 x^{4}}{35 y^{4}}$ $(9x^4)/(35y^4)$ is already in its simplest form, we leave it alone.

$\frac{15 x y}{3 x^{4} y^{2}}$ $(15xy)/(3x^4y^2)$ is NOT in its simplest form. The numerator and the denominator shares $x y$ $xy$ as their common factor. We multiply $\frac{15 x y}{3 x^{4} y^{2}}$ $(15xy)/(3x^4y^2)$ by $\frac{\frac{1}{x y}}{\frac{1}{x y}}$ $(1/(xy))/(1/(xy))$ to get $\frac{15}{3 x^{3} y}$ $(15)/(3x^3y)$

Now, we cross-simplify $\frac{9 x^{4}}{35 y^{4}}$ $(9x^4)/(35y^4)$ and $\frac{15}{3 x^{3} y}$ $(15)/(3x^3y)$ . The main question here is this: What is the GCF between $9 x^{4}$ $9x^4$ and $3 x^{3} y$ $3x^3y$ ? What about $35 y^{4}$ $35y^4$ and $15$ $15$ ?

The GCF between $9 x^{4}$ $9x^4$ and $3 x^{3} y$ $3x^3y$ is $3 x^{3}$ $3x^3$ , so divide $9 x^{4}$ $9x^4$ and $3 x^{3} y$ $3x^3y$ by $3 x^{3}$ $3x^3$ to get $3 x$ $3x$ and $y$ $y$

We now have $\frac{3 x}{35 y^{4}} \times \frac{15}{y}$ $(3x)/(35y^4)xx15/y$

Our next task is to find the GCF between $35 y^{4}$ $35y^4$ and $15$ $15$ ,which is $5$ $5$ . Divide $35 y^{4}$ $35y^4$ and $15$ $15$ by $5$ $5$ to get $7 y^{4}$ $7y^4$ and $3$ $3$ .

Now, the original expression becomes $\frac{3 x}{7 y^{4}} \times \frac{3}{y}$ $(3x)/(7y^4)xx3/y$

Multiply like we would multiply any other fraction to get $\frac{9 x}{7 y^{5}}$ $(9x)/(7y^5)$ . That is the answer!

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How do you simplify $\frac{9 x^{4}}{35 y^{4}} \cdot \frac{15 x y}{3 x^{4} y^{2}}$ $\frac { 9x ^ { 4} } { 35y ^ { 4} } \cdot \frac { 15x y } { 3x ^ { 4} y ^ { 2} }$ ?

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How do you simplify $\frac{9 x^{4}}{35 y^{4}} \cdot \frac{15 x y}{3 x^{4} y^{2}}$ $\frac { 9x ^ { 4} } { 35y ^ { 4} } \cdot \frac { 15x y } { 3x ^ { 4} y ^ { 2} }$ ?