The value of `((0.7)^0 - (0.1)^(-1))/((3/8)^(-1) (3/2)^(3) +(-1/3)^(-1))` is

Options

A. `-3/2`
B. `2/3`
C. `3`
D. 2

Answer

To solve the expression

\[ \frac{(0.7)^0 - (0.1)^{-1}}{(3/8)^{-1} \cdot (3/2)^{3} + (-1/3)^{-1}}, \]

we will break it down step by step.

### Step 1: Simplify the numerator

1. **Calculate \((0.7)^0\)**:
\[ (0.7)^0 = 1 \quad \text{(Any non-zero number raised to the power of 0 is 1)} \]

2. **Calculate \((0.1)^{-1}\)**:
\[ (0.1)^{-1} = \frac{1}{0.1} = 10 \quad \text{(Negative exponent means reciprocal)} \]

3. **Combine the results**:
\[ (0.7)^0 - (0.1)^{-1} = 1 - 10 = -9 \]

### Step 2: Simplify the denominator

1. **Calculate \((3/8)^{-1}\)**:
\[ (3/8)^{-1} = \frac{8}{3} \quad \text{(Negative exponent means reciprocal)} \]

2. **Calculate \((3/2)^{3}\)**:
\[ (3/2)^{3} = \frac{3^3}{2^3} = \frac{27}{8} \]

3. **Combine the results**:
\[ (3/8)^{-1} \cdot (3/2)^{3} = \frac{8}{3} \cdot \frac{27}{8} = \frac{27}{3} = 9 \]

4. **Calculate \((-1/3)^{-1}\)**:
\[ (-1/3)^{-1} = -3 \quad \text{(Negative exponent means reciprocal)} \]

5. **Combine the results in the denominator**:
\[ 9 + (-3) = 9 - 3 = 6 \]

### Step 3: Combine the numerator and denominator

Now we can substitute back into the original expression:
\[ \frac{-9}{6} \]

### Step 4: Simplify the fraction

1. **Simplify \(\frac{-9}{6}\)**:
\[ \frac{-9}{6} = \frac{-3}{2} \quad \text{(Dividing both numerator and denominator by 3)} \]

### Final Answer

Thus, the value of the expression is:

\[ \boxed{-\frac{3}{2}} \]

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