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Complete the equation by supplying the missing exponent:

[tex]\[3^1 \cdot 3^{-6} = 3^x\][/tex]

A. [tex]\(8\)[/tex]

B. [tex]\(-3\)[/tex]

C. [tex]\(4\)[/tex]

D. [tex]\(-8\)[/tex]

Sagot :

GinnyAnswer
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].
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