To rewrite [tex]\( 6^{-2} \)[/tex] without using an exponent, follow these steps:
1. Understand the Negative Exponent: Recall the property of exponents that states [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex]. Here, [tex]\( 6^{-2} \)[/tex] means [tex]\( \frac{1}{6^2} \)[/tex].
2. Rewrite the Expression: So [tex]\( 6^{-2} \)[/tex] can be rewritten as [tex]\( \frac{1}{6^2} \)[/tex].
3. Calculate the Denominator: Compute [tex]\( 6^2 \)[/tex] (6 raised to the power of 2), which is [tex]\( 6 \times 6 \)[/tex]. This gives:
[tex]\[
6^2 = 36
\][/tex]
4. Form the Fraction: Now substitute this result back into the fraction:
[tex]\[
\frac{1}{6^2} \implies \frac{1}{36}
\][/tex]
5. Express as a Decimal (if needed): If you need the result in decimal form, divide 1 by 36:
[tex]\[
\frac{1}{36} \approx 0.027777777777777776
\][/tex]
Therefore, [tex]\( 6^{-2} \)[/tex] can be rewritten without an exponent as:
[tex]\[
\frac{1}{36}
\][/tex]
And in decimal form, this is approximately:
[tex]\[
0.027777777777777776
\][/tex]
