Answer :

Sure! Let's break down the problem step-by-step using the properties of exponents.

We have the expression:

[tex]\[ x^9 \cdot x^{-4} \][/tex]

When you multiply expressions with the same base, you can add their exponents. This is a key property of exponents:

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

In this case, the base is [tex]\(x\)[/tex], and the exponents are 9 and -4. Let's apply the property:

1. Identify the exponents: Here, [tex]\(m = 9\)[/tex] and [tex]\(n = -4\)[/tex].

2. Add the exponents:

[tex]\[ 9 + (-4) = 9 - 4 = 5 \][/tex]

3. Write the result with the new exponent:

Since we have added the exponents, the expression simplifies to:

[tex]\[ x^5 \][/tex]

So, the final result for the expression [tex]\( x^9 \cdot x^{-4} \)[/tex] is [tex]\( x^5 \)[/tex].

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Rewritten by : Barada