Answer:
The answer is 3/5x^6y^6
Step-by-step explanation:
The given expression is:
-9x^-1 y^-9/-15x^5 y^-3
It can be written as:
= -9/-15 * x^-1/x^5 * y^-9/y^-3
As we know that [x^m/x^n = x^m-n]
= 3/5 * x^-1-5 * y^-9+3
= 3/5 * x^-6 * y^-6
= 3/5 * 1/x^6 * 1/y^6
= 3/5x^6y^6
The answer is 3/5x^6y^6....
The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
From the question, we are to determine the expression that is equivalent to the given expression
The given expression is
(-9x^-1 y^-9)/(-15x^5 y^-3)
This can be written as
[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]
[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]
This becomes
[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]
[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]
[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]
= [tex]\frac{3}{5x^{6}y^{6} }[/tex]
= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Learn more on Evaluating an expression here: https://brainly.com/question/3996169
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