Question

Simplify the expression answer should have a positive exponent six to the third power and parentheses to the times to the second power times six to the -4th power over six to the second power

Answer 1

To simplify the expression \((6^3 \cdot 2^2 \cdot 6^{-4}) / 6^2\), we can follow these steps:

1. **Combine the powers of 6 in the numerator**:
\[
6^3 \cdot 6^{-4} = 6^{3 + (-4)} = 6^{-1}
\]

2. **Now, the expression looks like**:
\[
\frac{6^{-1} \cdot 2^2}{6^2}
\]

3. **Subtract the exponent in the denominator from the exponent in the numerator**:
\[
\frac{6^{-1}}{6^2} = 6^{-1 - 2} = 6^{-3}
\]

4. **Now include the \(2^2\) from the numerator**:
\[
2^2 \cdot 6^{-3} = 4 \cdot 6^{-3}
\]

5. **Since we want a positive exponent, we can rewrite \(6^{-3}\) as \(\frac{1}{6^3}\)**:
\[
= \frac{4}{6^3}
\]

6. **Now simplify \(\frac{4}{6^3}\)**:
\[
6^3 = 216, \quad \text{so}, \quad \frac{4}{216} = \frac{1}{54}
\]

Thus, the final simplified expression is:

\[
\frac{4}{216} \text{ or } \frac{1}{54}
\]

In summary,

\[
\frac{4}{6^3} \quad \text{or simply } \frac{1}{54}
\]