Question

14 to the third power times 27 to the negative seventh power to the zero power divided by 3 to the fourth power

Answer 1

To solve the expression \( \frac{14^3 \times 27^{-7}^0}{3^4} \), we can simplify it step by step.

1. Start with the exponent of zero:
- Any number raised to the power of zero is equal to 1 (as long as it's not zero). Hence:
\[
27^{-7}^0 = 1
\]

2. Now, substitute this back into the expression:
\[
\frac{14^3 \times 1}{3^4} = \frac{14^3}{3^4}
\]

3. Now we need to calculate \( 14^3 \) and \( 3^4 \):
- Calculate \( 14^3 \):
\[
14^3 = 14 \times 14 \times 14 = 196 \times 14 = 2744
\]

- Calculate \( 3^4 \):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 9 \times 9 = 81
\]

4. Now substitute these back into the simplified expression:
\[
\frac{14^3}{3^4} = \frac{2744}{81}
\]

5. So, the final answer is:
\[
\frac{2744}{81}
\]

Thus, the value of the expression is \( \frac{2744}{81} \).