(x^(-4)y^(2))^(-3)*x^(4)y^(2)

Apply Power Rule: Apply the power of a power rule to the first term. The power of a power rule states that (a^m)^n = a^(m*n). We will apply this rule to the term (x^(-4)y^(2))^(-3). (x^(-4)y^(2))^(-3) = x^(-4*-3)y^(2*-3) = x^(12)y^(-6)Multiply Terms: Multiply the simplified first term by the second term. Now we multiply x^(12)y^(-6) by x^(4)y^(2). x^(12)y^(-6) * x^(4)y^(2)Apply Product Rule: Apply the product of powers rule to the x terms and y terms separately. The product of powers rule states that a^m * a^n = a^(m+n) when the bases are the same. We will apply this rule to the x terms and y terms separately. x^(12) * x^(4) = x^(12+4) y^(-6) * y^(2) = y^(-6+2)Add Exponents: Perform the addition of exponents for both x and y. Now we add the exponents for x and y. x^(12+4) = x^(16) y^(-6+2) = y^(-4)Combine Results: Combine the results for x and y. Now we combine the results for x and y to get the final simplified expression. x^(16) * y^(-4)Check Simplifications: Check for any possible simplifications or errors. The expression x^(16) * y^(-4) is already in its simplest form, and there are no further simplifications possible. There are no math errors in the previous steps.

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$\left(x^{-4} y^{2}\right)^{-3} \cdot x^{4} y^{2}$

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Algebra 1

Multiplication with rational exponents

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\left(x^{-4} y^{2}\right)^{-3} \cdot x^{4} y^{2}

Apply Power Rule: Apply the power of a power rule to the first term. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . We will apply this rule to the term $(x^{-4}y^{2})^{-3}$ . $\newline$ $(x^{-4}y^{2})^{-3} = x^{-4*-3}y^{2*-3}$ $\newline$ = $x^{12}y^{-6}$
Multiply Terms: Multiply the simplified first term by the second term. $\newline$ Now we multiply $x^{12}y^{-6}$ by $x^{4}y^{2}$ . $\newline$ $x^{12}y^{-6} \times x^{4}y^{2}$
Apply Product Rule: Apply the product of powers rule to the $x$ terms and $y$ terms separately. $\newline$ The product of powers rule states that $a^m \cdot a^n = a^{(m+n)}$ when the bases are the same. We will apply this rule to the $x$ terms and $y$ terms separately. $\newline$ $x^{12} \cdot x^{4} = x^{(12+4)}$ $\newline$ $y^{-6} \cdot y^{2} = y^{(-6+2)}$
Add Exponents: Perform the addition of exponents for both $x$ and $y$ . Now we add the exponents for $x$ and $y$ . $x^{(12+4)} = x^{16}$ $y^{(-6+2)} = y^{-4}$
Combine Results: Combine the results for $x$ and $y$ . Now we combine the results for $x$ and $y$ to get the final simplified expression. $x^{16} \cdot y^{-4}$
Check Simplifications: Check for any possible simplifications or errors. $\newline$ The expression $x^{16} \cdot y^{-4}$ is already in its simplest form, and there are no further simplifications possible. There are no math errors in the previous steps.