Solve the Expression: (35xy^7)/(7xy) × (8x)/(5y) Simplified

To solve this problem, follow these steps:

Step 1: Simplify the first fraction:

The first expression is $\frac{35x \cdot y^7}{7xy}$.

• Cancel the common factor of $7$: $35 \div 7 = 5$.

• This simplifies to $\frac{5x \cdot y^7}{x \cdot y}$.

• Cancel the common factor of $x$: $x/x$ cancels to $1$.

• Cancel part of the $y$ terms: $y^7/y = y^{7-1} = y^6$.

• The result is $5y^6$.

Step 2: Simplify the second fraction:

The second expression is $\frac{8x}{5y}$.

• No common factors in the numerator and denominator, so it remains $\frac{8x}{5y}$.

Step 3: Multiply these simplified results:

Now, multiply the results from Step 1 and Step 2: $5y^6 \cdot \frac{8x}{5y}$.

• The factor of $5$ in $5y^6$ and $\frac{8x}{5y}$ cancels: $5/5 = 1$.

• This results in $y^6 \cdot \frac{8x}{y}$.

• Cancel part of the $y$ terms: $y^6/y = y^{6-1} = y^5$.

Thus, the simplified expression is $8xy^5$.

Therefore, the solution to the problem is $\mathbf{8xy^5}$.