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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 for the product of [tex]\(2^9 \cdot 2^{-2}\)[/tex], we can make use of the exponent rules. Specifically, when multiplying two expressions with the same base, we add their exponents.

Here, we have:
[tex]$ 2^9 \cdot 2^{-2} $[/tex]

Step 1: Add the exponents since the base (2) is the same.
[tex]\[9 + (-2) = 7\][/tex]

Step 2: Write the result in exponential form:
[tex]\[2^7\][/tex]

Thus, the product [tex]\(2^9 \cdot 2^{-2}\)[/tex] simplifies to [tex]\(2^7\)[/tex].

Now, to find the numerical value of [tex]\(2^7\)[/tex]:
[tex]\[2^7 = 128\][/tex]

So, the product is:
[tex]\[ \boxed{2^7 = 128} \][/tex]
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