Sure, we want to find the value of [tex]\( 6^{-2} \)[/tex].
1. Understanding Negative Exponents:
- A negative exponent means that we take the reciprocal of the base raised to the positive exponent. So, [tex]\( 6^{-2} \)[/tex] can be rewritten as:
[tex]\[
6^{-2} = \frac{1}{6^2}
\][/tex]
2. Calculating the Positive Exponent:
- Next, we need to calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 6 \times 6 = 36
\][/tex]
3. Taking the Reciprocal:
- Now, we take the reciprocal of 36:
[tex]\[
\frac{1}{36}
\][/tex]
So, [tex]\( 6^{-2} \)[/tex] simplifies to [tex]\( \frac{1}{36} \)[/tex].
4. Decimal Form:
- Finally, converting [tex]\( \frac{1}{36} \)[/tex] to decimal form:
[tex]\[
\frac{1}{36} \approx 0.027777777777777776
\][/tex]
Thus, the value of [tex]\( 6^{-2} \)[/tex] is approximately [tex]\( 0.027777777777777776 \)[/tex].
