Select the equivalent expression. (x^(-3)yy)/(x^(-8)) (1)/(x^(5)y^(2)) x^(11)y^(2) x^(5)y^(2) (1)/(x^(11)y^(2))

Simplify Exponents: Simplify the expression using the properties of exponents. We have the expression (x^(-3)yy)/(x^(-8)). To simplify, we can use the property of exponents that states when we divide like bases, we subtract the exponents. So, x^(-3) / x^(-8) = x^(-3 - (-8)) = x^(5).Combine y Terms: Combine the y terms. Since there is no exponent specified for y in the numerator, we assume it is y^1. When we multiply like bases, we add the exponents. So, y^1 * y^1 = y^(1+1) = y^2.Combine x and y Terms: Combine the simplified x and y terms. From Step 1, we have x^(5), and from Step 2, we have y^(2). Multiplying these together gives us the simplified expression: x^(5)y^(2).Compare with Options: Compare the simplified expression with the given options. The simplified expression we found is x^(5)y^(2). We need to find the equivalent expression among the given options: (1)/(x^(5)y^(2)) x^(11)y^(2) x^(5)y^(2) (1)/(x^(11)y^(2)) The correct equivalent expression is x^(5)y^(2).

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Select the equivalent expression.

(x^(-3)yy)/(x^(-8))

(1)/(x^(5)y^(2))

x^(11)y^(2)

x^(5)y^(2)

(1)/(x^(11)y^(2))

Select the equivalent expression. $\newline$ $\frac{x^{-3} y y}{x^{-8}}$ $\newline$ $\frac{1}{x^{5} y^{2}}$ $\newline$ $x^{11} y^{2}$ $\newline$ $x^{5} y^{2}$ $\newline$ $\frac{1}{x^{11} y^{2}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-3} y y}{x^{-8}}

\newline

\frac{1}{x^{5} y^{2}}

\newline

x^{11} y^{2}

\newline

x^{5} y^{2}

\newline

\frac{1}{x^{11} y^{2}}

Simplify Exponents: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(x^{-3}yy)/(x^{-8})$ . To simplify, we can use the property of exponents that states when we divide like bases, we subtract the exponents. $\newline$ So, $x^{-3} / x^{-8} = x^{-3 - (-8)} = x^{5}$ .
Combine $y$ Terms: Combine the $y$ terms. $\newline$ Since there is no exponent specified for $y$ in the numerator, we assume it is $y^1$ . When we multiply like bases, we add the exponents. $\newline$ So, $y^1 \times y^1 = y^{(1+1)} = y^2$ .
Combine $x$ and $y$ Terms: Combine the simplified $x$ and $y$ terms. $\newline$ From Step $1$ , we have $x^{5}$ , and from Step $2$ , we have $y^{2}$ . Multiplying these together gives us the simplified expression: $\newline$ $x^{5}y^{2}$ .
Compare with Options: Compare the simplified expression with the given options. $\newline$ The simplified expression we found is $x^{5}y^{2}$ . We need to find the equivalent expression among the given options: $\newline$ $(1)/(x^{5}y^{2})$ $\newline$ $x^{11}y^{2}$ $\newline$ $x^{5}y^{2}$ $\newline$ $(1)/(x^{11}y^{2})$ $\newline$ The correct equivalent expression is $x^{5}y^{2}$ .