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Simplify [tex]\frac{x^{-9}}{x^{-12}}[/tex].

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GinnyAnswer
To simplify the expression \(\frac{x^{-9}}{x^{-12}}\), we need to apply the properties of exponents. Specifically, we use the rule:

[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]

In this case, our base \(a\) is \(x\), and our exponents are \(-9\) and \(-12\). Thus, we can rewrite the expression as:

[tex]\[ \frac{x^{-9}}{x^{-12}} = x^{-9 - (-12)} \][/tex]

Next, we need to simplify the exponent. Subtracting \(-12\) is the same as adding 12:

[tex]\[ -9 - (-12) = -9 + 12 \][/tex]

So, we perform the arithmetic:

[tex]\[ -9 + 12 = 3 \][/tex]

Therefore, the simplified form of the expression is:

[tex]\[ x^3 \][/tex]

So, the final result is:

[tex]\[ \frac{x^{-9}}{x^{-12}} = x^3 \][/tex]
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