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(-2x^(2)y^(7))^(5)

$\left(-2 x^{2} y^{7}\right)^{5}$

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Evaluate rational exponents

Full solution

Q.

\left(-2 x^{2} y^{7}\right)^{5}

Identify base and exponent: Identify the base and the exponent in the expression. $(-2x^{2}y^{7})^{5}$ has a base of $-2x^{2}y^{7}$ and an exponent of $5$ .
Apply power of product rule: Apply the power of a product rule: $(ab)^n = a^n * b^n$ . $(-2x^{2}y^{7})^5 = (-2)^5 * (x^2)^5 * (y^7)^5$ .
Calculate each part: Calculate each part: $\newline$ $(-2)^5 = -32$ , $\newline$ $(x^2)^5 = x^{(2*5)} = x^{10}$ , $\newline$ $(y^7)^5 = y^{(7*5)} = y^{35}$ .
Combine results: Combine the results: $\newline$ $-32 \times x^{10} \times y^{35}$ .

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