`(frac(-3)(4))^(-3)=` ?

Options

A. (a) `frac(27)(64)`
B. (b) `frac(64)(27)`
C. (c) `frac(-27)(64)`
D. (d) `frac(-64)(27)`

Answer

To solve the expression \((\frac{-3}{4})^{-3}\), we can follow these steps:

### Step 1: Rewrite the expression using the property of negative exponents
Using the property of negative exponents, we can rewrite the expression as:
\[ (\frac{-3}{4})^{-3} = \frac{1}{(\frac{-3}{4})^{3}} \]

### Step 2: Calculate the cube of the fraction
Now we need to calculate \((\frac{-3}{4})^{3}\):
\[ (\frac{-3}{4})^{3} = \frac{(-3)^{3}}{(4)^{3}} = \frac{-27}{64} \]

### Step 3: Substitute back into the expression
Now we substitute back into our expression from Step 1:
\[ \frac{1}{(\frac{-3}{4})^{3}} = \frac{1}{\frac{-27}{64}} = \frac{64}{-27} \]

### Step 4: Simplify the fraction
This can be simplified to:
\[ \frac{64}{-27} = -\frac{64}{27} \]

### Final Answer
Thus, the final answer is:
\[ -\frac{64}{27} \]

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