The expression (x^(-2)y^((1)/(2)))/(x^((1)/(3))y^(-1)), where x > 1 and y > 1, is

Combine x terms: We have the expression (x^(-2)y^(1/2))/(x^(1/3)y^(-1)). To simplify, we will use the properties of exponents to combine the x terms and the y terms separately.Simplify x terms: First, we simplify the x terms using the property of exponents that states when dividing like bases, we subtract the exponents: x^a / x^b = x^(a-b). So, for the x terms, we have x^(-2) / x^(1/3) = x^(-2 - 1/3).Simplify y terms: To subtract the exponents, we need a common denominator. The common denominator for 2 (which is 2/1) and 1/3 is 3. So we convert -2 to -6/3 to get the same denominator as 1/3. Now we have x^(-6/3 - 1/3) = x^(-7/3).Combine y terms: Next, we simplify the y terms using the same property of exponents: y^(1/2) / y^(-1) = y^(1/2 + 1).Combine x and y terms: Adding the exponents for y terms, we get y^(1/2 + 2/2) = y^(3/2).Final expression: Now we combine the simplified x and y terms to get the final simplified expression: x^(-7/3) * y^(3/2).Problem completion: Since the question prompt asks for the expression to be simplified and we have done so, we have completed the problem.

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The expression
(x^(-2)y^((1)/(2)))/(x^((1)/(3))y^(-1)), where
x > 1 and
y > 1, is

The expression $\frac{x^{-2} y^{\frac{1}{2}}}{x^{\frac{1}{3}} y^{-1}}$ , where x>1 and y>1 , is

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\frac{x^{-2} y^{\frac{1}{2}}}{x^{\frac{1}{3}} y^{-1}}

, where

x>1

and

y>1

, is

Combine $x$ terms: We have the expression $\frac{x^{-2}y^{\frac{1}{2}}}{x^{\frac{1}{3}}y^{-1}}$ . To simplify, we will use the properties of exponents to combine the $x$ terms and the $y$ terms separately.
Simplify $x$ terms: First, we simplify the $x$ terms using the property of exponents that states when dividing like bases, we subtract the exponents: $\frac{x^a}{x^b} = x^{(a-b)}$ . So, for the $x$ terms, we have $\frac{x^{-2}}{x^{\frac{1}{3}}} = x^{(-2 - \frac{1}{3})}$ .
Simplify $y$ terms: To subtract the exponents, we need a common denominator. The common denominator for $2$ (which is $\frac{2}{1}$ ) and $\frac{1}{3}$ is $3$ . So we convert $-2$ to $-\frac{6}{3}$ to get the same denominator as $\frac{1}{3}$ . Now we have $x^{(-\frac{6}{3} - \frac{1}{3})} = x^{(-\frac{7}{3})}$ .
Combine y terms: Next, we simplify the y terms using the same property of exponents: $y^{1/2} / y^{-1} = y^{1/2 + 1}$ .
Combine $x$ and $y$ terms: Adding the exponents for $y$ terms, we get $y^{(1/2 + 2/2)} = y^{3/2}$ .
Final expression: Now we combine the simplified $x$ and $y$ terms to get the final simplified expression: $x^{(-7/3)} \cdot y^{(3/2)}$ .
Problem completion: Since the question prompt asks for the expression to be simplified and we have done so, we have completed the problem.