Select the equivalent expression. (x^(8)y^(-5)y^(-8))/(x^(6)) (1)/(x^(2)) (x^(2))/(y^(13)) (y^(13))/(x^(2)) x^(2)

Use Exponent Property: To simplify the given expression, we will use the properties of exponents. The first property we will use is that when dividing powers with the same base, we subtract the exponents: a^(m)/a^(n) = a^(m-n).Simplify x Term: Applying this property to the x terms, we get x^(8-6) = x^(2).Combine y Terms: Now, we will combine the y terms using the property that when we multiply powers with the same base, we add the exponents: a^(m) * a^(n) = a^(m+n).Combine x and y Terms: Combining the y terms, we get y^(-5 + (-8)) = y^(-13).Rewrite Expression: Putting the simplified x and y terms together, we have x^(2) * y^(-13).Since y^(-13) is in the denominator, we can rewrite the expression as (x^(2))/(y^(13)).

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Find derivatives of using multiple formulae

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Q. Select the equivalent expression.

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\frac{x^{8} y^{-5} y^{-8}}{x^{6}}

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\frac{1}{x^{2}}

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\frac{x^{2}}{y^{13}}

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\frac{y^{13}}{x^{2}}

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x^{2}

Use Exponent Property: To simplify the given expression, we will use the properties of exponents. The first property we will use is that when dividing powers with the same base, we subtract the exponents: $a^{m}/a^{n} = a^{(m-n)}$ .
Simplify $x$ Term: Applying this property to the $x$ terms, we get $x^{(8-6)} = x^{2}$ .
Combine $y$ Terms: Now, we will combine the $y$ terms using the property that when we multiply powers with the same base, we add the exponents: $a^{m} \times a^{n} = a^{m+n}$ .
Combine $x$ and $y$ Terms: Combining the $y$ terms, we get $y^{(-5 + (-8))} = y^{-13}$ .
Rewrite Expression: Putting the simplified $x$ and $y$ terms together, we have $x^{2} \cdot y^{-13}$ .
Rewrite Expression: Putting the simplified $x$ and $y$ terms together, we have $x^{2} \cdot y^{-13}$ .Since $y^{-13}$ is in the denominator, we can rewrite the expression as $(x^{2})/(y^{13})$ .