2. $$ \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} $$

Question

UpStudy AI · Accepted Answer

Let's simplify the expression step by step:

$$
\frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}}
$$

### Step 1: Simplify the Denominator

First, expand the denominator $$\left(x y^{2}\right)^{3}$$ using the power of a product rule $$(ab)^n = a^n b^n$$:

$$
\left(x y^{2}\right)^{3} = x^{3} \left(y^{2}\right)^{3} = x^{3} y^{6}
$$

So, the expression becomes:

$$
\frac{35 x^{7} y^{8}}{7 x^{3} y^{6}}
$$

### Step 2: Simplify the Coefficients

Divide the numerical coefficients:

$$
\frac{35}{7} = 5
$$

### Step 3: Simplify the Variables

Apply the laws of exponents to simplify $$x$$ and $$y$$:

$$
x^{7} \div x^{3} = x^{7-3} = x^{4}
$$
$$
y^{8} \div y^{6} = y^{8-6} = y^{2}
$$

### Step 4: Combine the Simplified Parts

Putting it all together:

$$
5 x^{4} y^{2}
$$

### Final Simplified Expression

$$
5x^{4} y^{2}
$$
The simplified expression is $$5x^{4} y^{2}$$.

2. \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \)