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Complete the equation by supplying the missing exponent.

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

A. [tex]\( 2 \)[/tex]
B. [tex]\( 8 \)[/tex]
C. [tex]\( -3 \)[/tex]
D. [tex]\( -8 \)[/tex]

Sagot :

GinnyAnswer
Sure, let's solve the equation step-by-step.

We start with the given equation:

[tex]\[ 3^{-1} \cdot 3^{-6} = 3^2 \][/tex]

First, we use the property of exponents that states:

[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]

Applying this to the left side of the equation, we get:

[tex]\[ 3^{-1} \cdot 3^{-6} = 3^{-1 + (-6)} = 3^{-7} \][/tex]

So, our equation now looks like this:

[tex]\[ 3^{-7} = 3^2 \][/tex]

For the two sides of the equation to be equal, the exponents must also be equal. Therefore, we have:

[tex]\[ -7 = 2 \][/tex]

This shows that the missing exponent that completes the equation is indeed:

[tex]\[ -7 \][/tex]

So, the correct answer to complete the equation is:

[tex]\[ -7 \][/tex]
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