To complete the equation [tex]\(3^1 \cdot 3^{-6} = 3^x\)[/tex], we need to determine the missing exponent [tex]\(x\)[/tex].
1. Consider the expression on the left side of the equation: [tex]\(3^1 \cdot 3^{-6}\)[/tex].
2. Use the property of exponents that states [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]. In this context:
[tex]\[
3^1 \cdot 3^{-6} = 3^{1 + (-6)}
\][/tex]
3. Simplify the exponent:
[tex]\[
1 + (-6) = -5
\][/tex]
4. Therefore, the equation should be:
[tex]\[
3^1 \cdot 3^{-6} = 3^{-5}
\][/tex]
So, the missing exponent [tex]\(x\)[/tex] should be [tex]\(-5\)[/tex].
