College

Simplify the expression:

[tex] \left(\frac{5}{6}\right)^2 \cdot \frac{12}{25} [/tex]

Answer :

Sure, let's solve the problem step-by-step.

We are given the expression:
[tex]\[
\left(\frac{5}{6}\right)^2 \cdot \frac{12}{25}
\][/tex]

### Step 1: Square the Fraction
First, we need to square the fraction [tex]\(\frac{5}{6}\)[/tex].

[tex]\[
\left(\frac{5}{6}\right)^2 = \frac{5^2}{6^2} = \frac{25}{36}
\][/tex]

### Step 2: Multiply by Another Fraction
Next, we will multiply [tex]\(\frac{25}{36}\)[/tex] by [tex]\(\frac{12}{25}\)[/tex].

[tex]\[
\frac{25}{36} \cdot \frac{12}{25}
\][/tex]

### Step 3: Multiply the Numerators and Denominators
We multiply the numerators (top numbers) and the denominators (bottom numbers):

[tex]\[
\frac{25 \cdot 12}{36 \cdot 25}
\][/tex]

### Step 4: Simplify the Fraction
Notice that the 25 in the numerator and denominator cancels out:

[tex]\[
\frac{12}{36}
\][/tex]

We simplify [tex]\(\frac{12}{36}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 12:

[tex]\[
\frac{12 \div 12}{36 \div 12} = \frac{1}{3}
\][/tex]

So, the final simplified result is:

[tex]\[
\frac{1}{3}
\][/tex]

In decimal form:

[tex]\[
\frac{1}{3} \approx 0.33333333333333337
\][/tex]

Therefore, the final answer is:

[tex]\[
\frac{1}{3} \approx 0.33333333333333337
\][/tex]