Simplify. (-y^(2)z^(4))^(2)(3x^(2)y^(3)z)

Simplify Exponents: First, let's simplify (-y^(2)z^(4))^(2). We need to square both the y and z terms. (-y^(2))^2 = y^(2*2) = y^4 (z^(4))^2 = z^(4*2) = z^8 So, (-y^(2)z^(4))^(2) = y^4z^8Multiply Terms: Now, multiply y^4z^8 by 3x^(2)y^(3)z. We combine like terms by adding the exponents for y and z. y^4 * y^3 = y^(4+3) = y^7 z^8 * z = z^(8+1) = z^9 And multiply the coefficients: 1 * 3 = 3 So, y^4z^8 * 3x^(2)y^(3)z = 3x^(2)y^7z^9Check for Errors: Now we check for any math errors in the previous steps. Everything looks correct, so we can conclude that the simplified form is 3x^(2)y^7z^9.

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Simplify.

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

Simplify. $\newline$ $\left(-y^{2} z^{4}\right)^{2}\left(3 x^{2} y^{3} z\right)$

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Q. Simplify.

\newline

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

Simplify Exponents: First, let's simplify $(-y^{2}z^{4})^{2}$ . We need to square both the $y$ and $z$ terms. $\newline$ $(-y^{2})^{2} = y^{2*2} = y^4$ $\newline$ $(z^{4})^{2} = z^{4*2} = z^8$ $\newline$ So, $(-y^{2}z^{4})^{2} = y^4z^8$
Multiply Terms: Now, multiply $y^4z^8$ by $3x^{2}y^{3}z$ . We combine like terms by adding the exponents for $y$ and $z$ . $y^4 \cdot y^3 = y^{4+3} = y^7$ $z^8 \cdot z = z^{8+1} = z^9$ And multiply the coefficients: $1 \cdot 3 = 3$ So, $y^4z^8 \cdot 3x^{2}y^{3}z = 3x^{2}y^7z^9$
Check for Errors: Now we check for any math errors in the previous steps. $\newline$ Everything looks correct, so we can conclude that the simplified form is $3x^{2}y^{7}z^{9}.$