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Let’s check out your problem:

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

(−2x2y7)5 \left(-2 x^{2} y^{7}\right)^{5}

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Evaluate rational exponentsright chevron icon

Full solution

Q. (−2x2y7)5 \left(-2 x^{2} y^{7}\right)^{5}
  1. Identify base and exponent: Identify the base and the exponent in the expression. (−2x2y7)5(-2x^{2}y^{7})^{5} has a base of −2x2y7-2x^{2}y^{7} and an exponent of 55.
  2. Apply power of product rule: Apply the power of a product rule: (ab)n=an∗bn (ab)^n = a^n * b^n . (−2x2y7)5=(−2)5∗(x2)5∗(y7)5 (-2x^{2}y^{7})^5 = (-2)^5 * (x^2)^5 * (y^7)^5 .
  3. Calculate each part: Calculate each part:\newline(−2)5=−32(-2)^5 = -32,\newline(x2)5=x(2∗5)=x10(x^2)^5 = x^{(2*5)} = x^{10},\newline(y7)5=y(7∗5)=y35(y^7)^5 = y^{(7*5)} = y^{35}.
  4. Combine results: Combine the results:\newline−32×x10×y35-32 \times x^{10} \times y^{35}.

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