Question

Determine the value of the expression 4 to the 3 power multiply 4 to the negative 6 power

Answer 1

To simplify the expression \(4^3 \times 4^{-6}\), we can use the property of exponents that states:

\[
a^m \times a^n = a^{m+n}
\]

In this case, let \(a = 4\), \(m = 3\), and \(n = -6\). Applying the property:

\[
4^3 \times 4^{-6} = 4^{3 + (-6)} = 4^{-3}
\]

Next, we can simplify \(4^{-3}\) as follows:

\[
4^{-3} = \frac{1}{4^3}
\]

Now we need to calculate \(4^3\):

\[
4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
\]

Thus, we have:

\[
4^{-3} = \frac{1}{64}
\]

Therefore, the value of the expression \(4^3 \times 4^{-6}\) is:

\[
\boxed{\frac{1}{64}}
\]