`(0.04)^(-(1.5))` is equal to

Options

A. `25`
B. `125`
C. `60`
D. `5`

Answer

To solve the expression \((0.04)^{-1.5}\), we will follow these steps:

### Step 1: Rewrite the decimal as a fraction
We start by converting \(0.04\) into a fraction:
\[ 0.04 = \frac{4}{100} = \frac{1}{25} \]

### Step 2: Rewrite the expression with the fraction
Now we can rewrite the original expression:
\[ (0.04)^{-1.5} = \left(\frac{1}{25}\right)^{-1.5} \]

### Step 3: Apply the negative exponent rule
Using the rule that \(a^{-n} = \frac{1}{a^n}\), we can simplify:
\[ \left(\frac{1}{25}\right)^{-1.5} = \frac{1}{\left(\frac{1}{25}\right)^{1.5}} = 25^{1.5} \]

### Step 4: Rewrite \(25^{1.5}\)
Next, we can express \(25^{1.5}\) as:
\[ 25^{1.5} = 25^{\frac{3}{2}} = (25^{\frac{1}{2}})^3 \]

### Step 5: Calculate \(25^{\frac{1}{2}}\)
Now we find the square root of \(25\):
\[ 25^{\frac{1}{2}} = 5 \]

### Step 6: Raise the result to the power of 3
Finally, we raise \(5\) to the power of \(3\):
\[ (25^{\frac{1}{2}})^3 = 5^3 = 125 \]

### Conclusion
Thus, the value of \((0.04)^{-1.5}\) is:
\[ \boxed{125} \]

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