27. $$ \left(\frac{4}{7 y}\right)^{2} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \left(\frac{4}{7 y}\right)^{2} $$, follow these steps:

### Step 1: Apply the Exponent to Both the Numerator and the Denominator

When you raise a fraction to a power, you apply the exponent to both the numerator and the denominator separately:

$$
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
$$

Applying this to your expression:

$$
\left(\frac{4}{7 y}\right)^{2} = \frac{4^2}{(7 y)^2}
$$

### Step 2: Calculate the Powers

Calculate the squares:

$$
4^2 = 16
$$
$$
(7 y)^2 = 7^2 \cdot y^2 = 49 y^2
$$

### Step 3: Write the Simplified Form

Putting it all together:

$$
\frac{4^2}{(7 y)^2} = \frac{16}{49 y^2}
$$

### Final Answer

$$
\left(\frac{4}{7 y}\right)^{2} = \frac{16}{49 y^2}
$$
$$ \left(\frac{4}{7 y}\right)^{2} = \frac{16}{49 y^2} $$

27. \( \left(\frac{4}{7 y}\right)^{2} \)