Evaluate :
`(8^(-1) xx 5^(3) )/( 2^(-4) )`

Answer

To evaluate the expression \((8^{-1} \times 5^{3}) / (2^{-4})\), we can follow these steps:

### Step 1: Rewrite the base 8 in terms of base 2
We know that \(8\) can be expressed as \(2^3\). Therefore, we can rewrite \(8^{-1}\) as:
\[ 8^{-1} = (2^3)^{-1} = 2^{-3} \]

### Step 2: Substitute and simplify the expression
Now, substituting \(8^{-1}\) in the original expression gives us:
\[ \frac{(2^{-3} \times 5^{3})}{2^{-4}} \]

### Step 3: Apply the property of exponents
Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the expression:
\[ = 2^{-3} \times 5^{3} \times 2^{4} \]
This can be rewritten as:
\[ = 2^{-3 + 4} \times 5^{3} = 2^{1} \times 5^{3} \]

### Step 4: Calculate the values
Now, we can calculate \(2^{1}\) and \(5^{3}\):
\[ 2^{1} = 2 \]
\[ 5^{3} = 5 \times 5 \times 5 = 125 \]

### Step 5: Multiply the results
Finally, we multiply the results:
\[ 2 \times 125 = 250 \]

### Final Answer
Thus, the value of the expression \((8^{-1} \times 5^{3}) / (2^{-4})\) is:
\[ \boxed{250} \]

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