Select the equivalent expression. (y^(5)y^(2))/(x^(6)x^(3)) (y^(7))/(x^(9)) (x^(9))/(y^(7)) (1)/(x^(9)y^(3)) x^(9)y^(3)

Apply Exponent Properties: To find the equivalent expression, we need to simplify the given expression using the properties of exponents.Simplify Numerator: When multiplying powers with the same base, we add the exponents. So for the numerator y^(5)y^(2), we add the exponents 5 and 2. y^(5)y^(2) = y^(5+2) = y^(7)Simplify Denominator: Similarly, for the denominator x^(6)x^(3), we add the exponents 6 and 3. x^(6)x^(3) = x^(6+3) = x^(9)Combine Simplified Terms: Now we have the simplified form of the numerator and denominator. We can write the entire expression as: (y^(5)y^(2))/(x^(6)x^(3)) = y^(7)/x^(9)Identify Equivalent Expression: Comparing the simplified expression with the given options, we find that the equivalent expression is (y^(7))/(x^(9)).

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Q. Select the equivalent expression.

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\frac{y^{5} y^{2}}{x^{6} x^{3}}

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\frac{y^{7}}{x^{9}}

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\frac{x^{9}}{y^{7}}

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\frac{1}{x^{9} y^{3}}

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x^{9} y^{3}

Apply Exponent Properties: To find the equivalent expression, we need to simplify the given expression using the properties of exponents.
Simplify Numerator: When multiplying powers with the same base, we add the exponents. So for the numerator $y^{5}y^{2}$ , we add the exponents $5$ and $2$ . $\newline$ $y^{5}y^{2} = y^{5+2} = y^{7}$
Simplify Denominator: Similarly, for the denominator $x^{6}x^{3}$ , we add the exponents $6$ and $3$ . $\newline$ $x^{6}x^{3} = x^{6+3} = x^{9}$
Combine Simplified Terms: Now we have the simplified form of the numerator and denominator. We can write the entire expression as: $\newline$ $(y^{5}y^{2})/(x^{6}x^{3}) = y^{7}/x^{9}$
Identify Equivalent Expression: Comparing the simplified expression with the given options, we find that the equivalent expression is $(y^{7})/(x^{9})$ .