The problem asks to simplify the expression $\frac{0.084 \times 0.81}{0.027 \times 0.04}$ and express the result in standard form.

1. Problem Description

The problem asks to simplify the expression $\frac{0.084 \times 0.81}{0.027 \times 0.04}$ and express the result in standard form.

2. Solution Steps

First, let's rewrite the expression as a fraction:

$\frac{0.084 \times 0.81}{0.027 \times 0.04}$

To simplify the expression, we can rewrite each decimal as a fraction:

$0.084 = \frac{84}{1000}$

$0.81 = \frac{81}{100}$

$0.027 = \frac{27}{1000}$

$0.04 = \frac{4}{100}$

Substituting these values into the expression, we get:

$\frac{\frac{84}{1000} \times \frac{81}{100}}{\frac{27}{1000} \times \frac{4}{100}}$

This can be simplified as:

$\frac{84 \times 81}{1000 \times 100} \div \frac{27 \times 4}{1000 \times 100}$

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So,

$\frac{84 \times 81}{1000 \times 100} \times \frac{1000 \times 100}{27 \times 4}$

We can cancel out the common factors $1000$ and $100$:

$\frac{84 \times 81}{27 \times 4}$

Now we simplify the numbers:

$84 = 4 \times 21$

$81 = 27 \times 3$

So we have:

$\frac{4 \times 21 \times 27 \times 3}{27 \times 4}$

Cancel the common factors $4$ and $27$:

$21 \times 3 = 63$

Therefore, the simplified expression is $63$.

In standard form, this is $6.3 \times 10^1$.

3. Final Answer

$6.3 \times 10^1$