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Answer :
To simplify the expression [tex]\(x^9 \cdot x^8\)[/tex] using the product rule for exponents, you can follow these steps:
1. Identify the Base and the Exponents:
- Both terms in the expression have the same base, which is [tex]\(x\)[/tex].
- The exponents are 9 and 8 for [tex]\(x^9\)[/tex] and [tex]\(x^8\)[/tex], respectively.
2. Apply the Product Rule for Exponents:
- The product rule states that when you multiply like bases, you add the exponents. In other words, for any base [tex]\(x\)[/tex], [tex]\(x^a \cdot x^b = x^{a+b}\)[/tex].
3. Add the Exponents:
- Add the exponents 9 and 8 together: [tex]\(9 + 8 = 17\)[/tex].
4. Write the Simplified Expression:
- Using the result from adding the exponents, [tex]\((x^9 \cdot x^8)\)[/tex] simplifies to [tex]\(x^{17}\)[/tex].
So, the simplified expression is [tex]\(x^{17}\)[/tex].
1. Identify the Base and the Exponents:
- Both terms in the expression have the same base, which is [tex]\(x\)[/tex].
- The exponents are 9 and 8 for [tex]\(x^9\)[/tex] and [tex]\(x^8\)[/tex], respectively.
2. Apply the Product Rule for Exponents:
- The product rule states that when you multiply like bases, you add the exponents. In other words, for any base [tex]\(x\)[/tex], [tex]\(x^a \cdot x^b = x^{a+b}\)[/tex].
3. Add the Exponents:
- Add the exponents 9 and 8 together: [tex]\(9 + 8 = 17\)[/tex].
4. Write the Simplified Expression:
- Using the result from adding the exponents, [tex]\((x^9 \cdot x^8)\)[/tex] simplifies to [tex]\(x^{17}\)[/tex].
So, the simplified expression is [tex]\(x^{17}\)[/tex].
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