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

Answer

To evaluate the expression \(\left(-\frac{1}{4}\right)^{-3} \times \left(-\frac{1}{4}\right)^{2}\), we can follow these steps:

### Step 1: Apply the Property of Exponents
We know that when multiplying two powers with the same base, we can add the exponents. Here, the base is \(-\frac{1}{4}\).

\[ \left(-\frac{1}{4}\right)^{-3} \times \left(-\frac{1}{4}\right)^{2} = \left(-\frac{1}{4}\right)^{-3 + 2} \]

### Step 2: Simplify the Exponent
Now, simplify the exponent:

\[ -3 + 2 = -1 \]

So, we have:

\[ \left(-\frac{1}{4}\right)^{-1} \]

### Step 3: Apply the Negative Exponent Rule
According to the rule for negative exponents, \(\left(a\right)^{-n} = \frac{1}{a^n}\). Thus:

\[ \left(-\frac{1}{4}\right)^{-1} = \frac{1}{\left(-\frac{1}{4}\right)^{1}} = \frac{1}{-\frac{1}{4}} \]

### Step 4: Simplify the Fraction
To simplify \(\frac{1}{-\frac{1}{4}}\), we can multiply by the reciprocal:

\[ \frac{1}{-\frac{1}{4}} = -4 \]

### Final Answer
Thus, the value of the expression \(\left(-\frac{1}{4}\right)^{-3} \times \left(-\frac{1}{4}\right)^{2}\) is:

\[ \boxed{-4} \]

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