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Sagot :
Let's simplify the expression:
[tex]\[ \frac{a^{-5} b^{-4}}{a^{-13} b^8} \][/tex]
We start by using the properties of exponents. The properties of exponents tell us that when we divide powers with the same base, we subtract the exponents.
First, simplify the [tex]\(a\)[/tex] terms:
[tex]\[ \frac{a^{-5}}{a^{-13}} = a^{-5 - (-13)} = a^{-5 + 13} = a^8 \][/tex]
Next, simplify the [tex]\(b\)[/tex] terms:
[tex]\[ \frac{b^{-4}}{b^8} = b^{-4 - 8} = b^{-12} \][/tex]
So, combining these results, we get:
[tex]\[ \frac{a^{-5} b^{-4}}{a^{-13} b^8} = a^8 b^{-12} \][/tex]
Since [tex]\(b^{-12} = \frac{1}{b^{12}}\)[/tex], we can write the expression as:
[tex]\[ \frac{a^8}{b^{12}} \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \boxed{\frac{a^8}{b^{12}}} \][/tex]
[tex]\[ \frac{a^{-5} b^{-4}}{a^{-13} b^8} \][/tex]
We start by using the properties of exponents. The properties of exponents tell us that when we divide powers with the same base, we subtract the exponents.
First, simplify the [tex]\(a\)[/tex] terms:
[tex]\[ \frac{a^{-5}}{a^{-13}} = a^{-5 - (-13)} = a^{-5 + 13} = a^8 \][/tex]
Next, simplify the [tex]\(b\)[/tex] terms:
[tex]\[ \frac{b^{-4}}{b^8} = b^{-4 - 8} = b^{-12} \][/tex]
So, combining these results, we get:
[tex]\[ \frac{a^{-5} b^{-4}}{a^{-13} b^8} = a^8 b^{-12} \][/tex]
Since [tex]\(b^{-12} = \frac{1}{b^{12}}\)[/tex], we can write the expression as:
[tex]\[ \frac{a^8}{b^{12}} \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \boxed{\frac{a^8}{b^{12}}} \][/tex]
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