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QuestionFind the value of ∏\prod for the equivalent expression: 92y=∏10y9\frac{9}{2 y}=\frac{\prod}{10 y^{9}}.

Studdy Solution

STEP 1

Assumptions1. The two rational expressions are equivalent. . We are solving for the value of the numerator in the second fraction, which we will denote as "x".

STEP 2

To make two fractions equivalent, the ratio of the numerator to the denominator must be the same for both fractions. We can express this with the equation92y=x10y9\frac{9}{2y} = \frac{x}{10y^9}

STEP 3

To solve for x, we can cross multiply. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting this equal to the denominator of the first fraction multiplied by the numerator of the second fraction. This gives us9×10y9=2y×x9 \times10y^9 =2y \times x

STEP 4

olving for x, we divide both sides of the equation by2yx=9×10y92yx = \frac{9 \times10y^9}{2y}

STEP 5

implify the right side of the equation by cancelling out the common factor of yx=9×10y82x = \frac{9 \times10y^8}{2}

STEP 6

Further simplify the right side of the equation by performing the multiplicationx=90y82x = \frac{90y^8}{2}

STEP 7

Finally, simplify the right side of the equation by performing the divisionx =45y^So, to make the two rational expressions equivalent, the numerator of the second fraction should be 45y^.

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