To compute [tex]\( 27^{-3} \)[/tex]:
1. Understand that raising a number to a negative exponent means you take the reciprocal of the base raised to the positive exponent. So, [tex]\( 27^{-3} = \frac{1}{27^3} \)[/tex].
2. Calculate [tex]\( 27^3 \)[/tex]. To do this, you multiply 27 by itself three times:
[tex]\[
27^3 = 27 \times 27 \times 27
\][/tex]
3. Once you have the value of [tex]\( 27^3 \)[/tex], take the reciprocal of that number. In other words:
[tex]\[
27^{-3} = \frac{1}{27^3}
\][/tex]
4. Converting your final answer from fraction form to decimal gives:
[tex]\[
27^{-3} \approx 5.080526342529086 \times 10^{-5}
\][/tex]
So, [tex]\( 27^{-3} \approx 5.080526342529086e-05 \)[/tex].
