Find the value of `(27 xx t^(-4) )/( 3^(-2) xx 18 xx t^(-8) ) ( t ne 0)`.

Options

A. `(9)/(2) t^(4)`
B. `(27)/(2) t^(-4)`
C. `(27)/(2) t^(4)`
D. `(9)/(2) t^(-4)`

Answer

To find the value of the expression \((27 t^{-4}) / (3^{-2} \times 18 \times t^{-8})\), we can simplify it step by step.

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{27 t^{-4}}{3^{-2} \times 18 \times t^{-8}} \]

### Step 2: Simplify the denominator
First, we can simplify the denominator:
\[ 3^{-2} \times 18 = 3^{-2} \times (2 \times 9) = 3^{-2} \times (2 \times 3^2) = 2 \times 3^{2 - 2} = 2 \times 3^0 = 2 \]
So, the expression now looks like:
\[ \frac{27 t^{-4}}{2} \]

### Step 3: Simplify the powers of \( t \)
Next, we simplify the powers of \( t \):
\[ t^{-4} \div t^{-8} = t^{-4 - (-8)} = t^{-4 + 8} = t^{4} \]
Thus, the expression becomes:
\[ \frac{27 t^{4}}{2} \]

### Step 4: Final expression
Now, we can write the final simplified expression:
\[ \frac{27 t^{4}}{2} \]

### Conclusion
The value of the expression \((27 t^{-4}) / (3^{-2} \times 18 \times t^{-8})\) is:
\[ \frac{27 t^{4}}{2} \]

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