Simplify ((5y^2)/(15y^4))^-2

Math
(5y215y4)-2
Cancel the common factor of 5 and 15.
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Factor 5 out of 5y2.
(5(y2)15y4)-2
Cancel the common factors.
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Factor 5 out of 15y4.
(5(y2)5(3y4))-2
Cancel the common factor.
(5y25(3y4))-2
Rewrite the expression.
(y23y4)-2
(y23y4)-2
(y23y4)-2
Cancel the common factor of y2 and y4.
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Multiply by 1.
(y2⋅13y4)-2
Cancel the common factors.
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Factor y2 out of 3y4.
(y2⋅1y2(3y2))-2
Cancel the common factor.
(y2⋅1y2(3y2))-2
Rewrite the expression.
(13y2)-2
(13y2)-2
(13y2)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(3y2)2
Apply the product rule to 3y2.
32(y2)2
Raise 3 to the power of 2.
9(y2)2
Multiply the exponents in (y2)2.
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Apply the power rule and multiply exponents, (am)n=amn.
9y2⋅2
Multiply 2 by 2.
9y4
9y4
Simplify ((5y^2)/(15y^4))^-2

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