Simplify the following expressions :
`3/8 xx 9/16 xx 7/5`

Answer

To simplify the expression \( \frac{3}{8} \times \frac{9}{16} \times \frac{7}{5} \), we will follow these steps:

### Step 1: Write the expression in a single fraction
We can combine the fractions by multiplying the numerators together and the denominators together:
\[ \frac{3 \times 9 \times 7}{8 \times 16 \times 5} \]

### Step 2: Multiply the numerators
Now, we will multiply the numbers in the numerator:
\[ 3 \times 9 = 27 \]
\[ 27 \times 7 = 189 \]
So, the numerator is \( 189 \).

### Step 3: Multiply the denominators
Next, we will multiply the numbers in the denominator:
\[ 8 \times 16 = 128 \]
\[ 128 \times 5 = 640 \]
So, the denominator is \( 640 \).

### Step 4: Combine the results
Now we can write the combined fraction:
\[ \frac{189}{640} \]

### Step 5: Check for simplification
We need to check if \( \frac{189}{640} \) can be simplified. The numerator \( 189 \) factors into \( 3^3 \times 7 \) and the denominator \( 640 \) factors into \( 2^7 \times 5 \). Since there are no common factors, the fraction is already in its simplest form.

### Final Answer
Thus, the simplified expression is:
\[ \frac{189}{640} \]

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