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Fully simplify.

(-4x^(2)y^(5))^(3)
Answer:

Fully simplify. $\newline$ $\left(-4 x^{2} y^{5}\right)^{3}$ $\newline$ Answer:

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Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-4 x^{2} y^{5}\right)^{3}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-4x^{2}y^{5})^{3}$ . $\newline$ In $(-4x^{2}y^{5})^{3}$ , the base is $-4x^{2}y^{5}$ and the exponent is $3$ .
Apply power of product rule: Apply the power of a product rule, which states that $(ab)^n = a^n * b^n$ , to the base. $(-4x^{2}y^{5})^{3} = (-4)^3 * (x^{2})^3 * (y^{5})^3$
Calculate each part: Calculate each part separately. $\newline$ $(-4)^3 = -4 \times -4 \times -4 = -64$ $\newline$ $(x^{2})^3 = x^{(2\times3)} = x^{6}$ $\newline$ $(y^{5})^3 = y^{(5\times3)} = y^{15}$
Combine results: Combine the results from Step $3$ . $\newline$ $(-4x^{2}y^{5})^{3} = -64 \times x^{6} \times y^{15}$

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