8xy^(-2)×3x^(-3)y^(3)÷12 xy

Write Expression: Write down the original expression and prepare to simplify. We have the expression 8xy^(-2)×3x^(-3)y^(3)÷12xy. We will simplify this by combining like terms and using the properties of exponents.Combine Coefficients and Terms: Combine the coefficients and the like terms. First, we combine the coefficients (numbers in front of the variables): (8 * 3) / 12 = 24 / 12 = 2. Next, we combine the x terms: x * x^(-3) = x^(1-3) = x^(-2). Then, we combine the y terms: y^(-2) * y^(3) = y^(-2+3) = y^(1). Finally, we divide by the remaining xy in the denominator: x^(-2) / x = x^(-2-1) = x^(-3), and y / y = y^(1-1) = y^(0) = 1 (since any number to the power of 0 is 1).Write Simplified Expression: Write down the simplified expression. After combining like terms, we have 2 * x^(-3) * 1, which simplifies to 2x^(-3).

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Find derivatives of using multiple formulae

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8 x y^{-2} \times 3 x^{-3} y^{3} \div 12 x y

Write Expression: Write down the original expression and prepare to simplify. $\newline$ We have the expression $8xy^{-2}\times 3x^{-3}y^{3}\div 12xy$ . We will simplify this by combining like terms and using the properties of exponents.
Combine Coefficients and Terms: Combine the coefficients and the like terms. $\newline$ First, we combine the coefficients (numbers in front of the variables): $(8 \times 3) / 12 = 24 / 12 = 2$ . $\newline$ Next, we combine the $x$ terms: $x \times x^{-3} = x^{1-3} = x^{-2}$ . $\newline$ Then, we combine the $y$ terms: $y^{-2} \times y^{3} = y^{-2+3} = y^{1}$ . $\newline$ Finally, we divide by the remaining $xy$ in the denominator: $x^{-2} / x = x^{-2-1} = x^{-3}$ , and $y / y = y^{1-1} = y^{0} = 1$ (since any number to the power of $0$ is $1$ ).
Write Simplified Expression: Write down the simplified expression. $\newline$ After combining like terms, we have $2 \times x^{(-3)} \times 1$ , which simplifies to $2x^{(-3)}$ .