The simplified form of the expression using the law of exponent is 5/a^9b^9
Exponential expression
Given the exponential expression as shown:
[tex]\frac{25a^{-5}b^{-8}}{5a^4b}[/tex]
According to product and quotient of exponents, multiplication will be addition and quotient will be difference.
[tex]\frac{25a^{-5}b^{-8}}{5a^4b}=\frac{25}{5}a^{-5-4}b^{-8-1}\\ \frac{25a^{-5}b^{-8}}{5a^4b}=5a^{-9}b^{-9}[/tex]
Write the result as fraction
[tex]\frac{25a^{-5}b^{-8}}{5a^4b}=\frac{5}{a^9b^9}[/tex]
Hence the simplified form of the expression using the law of exponent is 5/a^9b^9
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