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Simplify the expression.

[tex]\[a^6 b^3 \cdot a^2 b^{-2}\][/tex]

A. [tex]\[\frac{a^{12}}{b^6}\][/tex]

B. [tex]\[a^4 b^5\][/tex]

C. [tex]\[a^8 b\][/tex]

D. [tex]\[a^8 b^5\][/tex]


Sagot :

Let's simplify the expression [tex]\(a^6 b^3 \cdot a^2 b^{-2}\)[/tex] step by step.

Step 1: Combine the powers of [tex]\(a\)[/tex].
- We have [tex]\(a^6\)[/tex] and [tex]\(a^2\)[/tex].
- When multiplying terms with the same base, we add their exponents: [tex]\[a^6 \cdot a^2 = a^{6+2} = a^8.\][/tex]

Step 2: Combine the powers of [tex]\(b\)[/tex].
- We have [tex]\(b^3\)[/tex] and [tex]\(b^{-2}\)[/tex].
- When multiplying terms with the same base, we add their exponents:
[tex]\[b^3 \cdot b^{-2} = b^{3 + (-2)} = b^{3-2} = b^1.\][/tex]

Step 3: Write down the simplified expression.
[tex]\[a^6 b^3 \cdot a^2 b^{-2} = a^8 b.\][/tex]

Thus, the simplified expression is [tex]\(\boxed{a^8 b}\)[/tex].

So, the correct answer is:
C. [tex]\(a^8 b\)[/tex]
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