Evaluate : `(9^(-1) xx 5^(3) )/( 3^(-3) )`

Options

A. 370
B. 315
C. 375
D. 400

Answer

To evaluate the expression \((9^{-1} \times 5^{3}) / (3^{-3})\), we will follow these steps:

### Step 1: Rewrite Negative Exponents
Recall that \(a^{-b} = \frac{1}{a^b}\). Therefore, we can rewrite \(9^{-1}\) and \(3^{-3}\):
\[ 9^{-1} = \frac{1}{9} \quad \text{and} \quad 3^{-3} = \frac{1}{3^3} \]
So, the expression becomes:
\[ \frac{\left(\frac{1}{9} \times 5^{3}\right)}{\left(\frac{1}{3^{3}}\right)} \]

### Step 2: Change Division to Multiplication
When we divide by a fraction, we can multiply by its reciprocal:
\[ \frac{1}{9} \times 5^{3} \times 3^{3} \]

### Step 3: Calculate \(5^3\) and \(3^3\)
Now, we calculate \(5^3\) and \(3^3\):
\[ 5^3 = 125 \quad \text{and} \quad 3^3 = 27 \]

### Step 4: Substitute Values
Substituting these values back into the expression gives:
\[ \frac{1}{9} \times 125 \times 27 \]

### Step 5: Simplify
Now, we can simplify:
\[ \frac{125 \times 27}{9} \]

### Step 6: Calculate \(125 \times 27\)
Calculating \(125 \times 27\):
\[ 125 \times 27 = 3375 \]

### Step 7: Divide by 9
Now we divide \(3375\) by \(9\):
\[ \frac{3375}{9} = 375 \]

### Final Answer
Thus, the value of the expression \((9^{-1} \times 5^{3}) / (3^{-3})\) is:
\[ \boxed{375} \]

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