Question

Determine the value of the expression 4^3x4^-6

4^-18
1/12
-64
1/64

Answer 1

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

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

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

\[
4^{-3} = \frac{1}{4^{3}} = \frac{1}{(4^2) \times 4} = \frac{1}{16 \times 4} = \frac{1}{64}
\]

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

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

Therefore, the answer is:

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