Select the equivalent expression. (y^(2))/(x^(7)x^(-5)y^(-2)) (y^(4))/(x^(2)) (x^(2))/(y^(4)) x^(12)y^(4) (1)/(x^(12)y^(4))

Combine Exponents Like Bases: Simplify the expression by combining the exponents of like bases using the properties of exponents. For the base x, we have x^(7) * x^(-5), which simplifies to x^(7-5) because when you multiply with the same base, you add the exponents. For the base y, we have y^(2) * y^(-2), which simplifies to y^(2-2) because when you multiply with the same base, you add the exponents.Calculate Exponents: Perform the calculations for the exponents. For the base x, we have x^(7-5) which equals x^(2). For the base y, we have y^(2-2) which equals y^(0).Remember Power of 0: Remember that any number raised to the power of 0 is 1. So, y^(0) equals 1.Combine Simplified Terms: Combine the simplified terms. Since y^(0) equals 1, it does not affect the expression when multiplied. The simplified expression is (1 * x^(2)) / (1 * 1), which is just x^(2).Compare with Options: Compare the simplified expression with the given options. The equivalent expression is (x^(2))/(y^(4)), which is not the same as our simplified expression x^(2).

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Select the equivalent expression.

(y^(2))/(x^(7)x^(-5)y^(-2))

(y^(4))/(x^(2))

(x^(2))/(y^(4))

x^(12)y^(4)

(1)/(x^(12)y^(4))

Select the equivalent expression. $\newline$ $\frac{y^{2}}{x^{7} x^{-5} y^{-2}}$ $\newline$ $\frac{y^{4}}{x^{2}}$ $\newline$ $\frac{x^{2}}{y^{4}}$ $\newline$ $x^{12} y^{4}$ $\newline$ $\frac{1}{x^{12} y^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{y^{2}}{x^{7} x^{-5} y^{-2}}

\newline

\frac{y^{4}}{x^{2}}

\newline

\frac{x^{2}}{y^{4}}

\newline

x^{12} y^{4}

\newline

\frac{1}{x^{12} y^{4}}

Combine Exponents Like Bases: Simplify the expression by combining the exponents of like bases using the properties of exponents. $\newline$ For the base $x$ , we have $x^{7} \times x^{-5}$ , which simplifies to $x^{7-5}$ because when you multiply with the same base, you add the exponents. $\newline$ For the base $y$ , we have $y^{2} \times y^{-2}$ , which simplifies to $y^{2-2}$ because when you multiply with the same base, you add the exponents.
Calculate Exponents: Perform the calculations for the exponents. $\newline$ For the base $x$ , we have $x^{(7-5)}$ which equals $x^{2}$ . $\newline$ For the base $y$ , we have $y^{(2-2)}$ which equals $y^{0}$ .
Remember Power of $0$ : Remember that any number raised to the power of $0$ is $1$ . So, $y^{0}$ equals $1$ .
Combine Simplified Terms: Combine the simplified terms. $\newline$ Since $y^{0}$ equals $1$ , it does not affect the expression when multiplied. $\newline$ The simplified expression is $(1 \times x^{2}) / (1 \times 1)$ , which is just $x^{2}$ .
Compare with Options: Compare the simplified expression with the given options. The equivalent expression is $(x^{2})/(y^{4})$ , which is not the same as our simplified expression $x^{2}$ .