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Find the product. Write your answer in exponential form.

[tex]2^9 \cdot 2^{-2}[/tex]

Enter the correct answer:

Sagot :

GinnyAnswer
To solve the problem [tex]\( 2^9 \cdot 2^{-2} \)[/tex], we will use the properties of exponents. Specifically, we will use the property that states:

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

In this case, our base [tex]\( a \)[/tex] is [tex]\( 2 \)[/tex], and the exponents are [tex]\( 9 \)[/tex] and [tex]\( -2 \)[/tex].

First, we add the exponents together:

[tex]\[ 9 + (-2) = 7 \][/tex]

This gives us:

[tex]\[ 2^{9 + (-2)} = 2^7 \][/tex]

Therefore, the product of [tex]\( 2^9 \)[/tex] and [tex]\( 2^{-2} \)[/tex] is:

[tex]\[ 2^7 \][/tex]

So the answer is:

[tex]\[ 2^7 \][/tex]
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