Solve(14 to the 3rd power times 27 to the -7 power) to the power of zero/ 3 to the 4th power with only positive exponents, then solve the expression. Your answer will be a simplified expression with no remaining exponents.

Answer 1

We start with the expression:

\[ \left(14^3 \times 27^{-7}\right)^0 \div 3^4 \]

According to the property of exponents, any non-zero number raised to the power of zero equals 1:

\[ \left(14^3 \times 27^{-7}\right)^0 = 1 \]

Now we can substitute that back into the expression:

\[ 1 \div 3^4 \]

Calculating \(3^4\):

\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

Now substitute that into the expression:

\[ 1 \div 81 = \frac{1}{81} \]

So the final simplified expression is:

\[ \frac{1}{81} \]

Thus, the answer is:

\[ \frac{1}{81} \]