Simplify the following a) ((x)/(y))^(3)×((y)/(z))^(2)×((z)/(x))^(4)

Combine like terms: Combine the powers of the same bases by adding or subtracting the exponents. ((x)/(y))^3 × ((y)/(z))^2 × ((z)/(x))^4 = x^3/y^3 × y^2/z^2 × z^4/x^4Simplify exponents: Simplify by combining like terms. = (x^3 * y^2 * z^4) / (y^3 * z^2 * x^4) = x^(3-4) * y^(2-3) * z^(4-2) = x^(-1) * y^(-1) * z^(2)Rewrite negative exponents: Rewrite negative exponents as fractions. = 1/x * 1/y * z^2 = z^2 / (x * y)

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Simplify the following
a)
((x)/(y))^(3)×((y)/(z))^(2)×((z)/(x))^(4)

Simplify the following $\newline$ $\left(\frac{x}{y}\right)^{3} \times\left(\frac{y}{z}\right)^{2} \times\left(\frac{z}{x}\right)^{4}$

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Grade 8

Writing from expanded to exponent form

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Q. Simplify the following

\newline

\left(\frac{x}{y}\right)^{3} \times\left(\frac{y}{z}\right)^{2} \times\left(\frac{z}{x}\right)^{4}

Combine like terms: Combine the powers of the same bases by adding or subtracting the exponents. $\newline$ $\left(\frac{x}{y}\right)^3 \times \left(\frac{y}{z}\right)^2 \times \left(\frac{z}{x}\right)^4 = \frac{x^3}{y^3} \times \frac{y^2}{z^2} \times \frac{z^4}{x^4}$
Simplify exponents: Simplify by combining like terms. $\newline$ $= \frac{x^3 \cdot y^2 \cdot z^4}{y^3 \cdot z^2 \cdot x^4}$ $\newline$ $= x^{3-4} \cdot y^{2-3} \cdot z^{4-2}$ $\newline$ $= x^{-1} \cdot y^{-1} \cdot z^{2}$
Rewrite negative exponents: Rewrite negative exponents as fractions. $\newline$ $= \frac{1}{x} \times \frac{1}{y} \times z^{2}$ $\newline$ $= \frac{z^{2}}{xy}$