Question
![Simplify:
(3x^5y^-7)^2
(9x^10)/(y^14)
(6x^10)/(y^14)
(1)/(9x^10)y^(14)
9(x^7)/(y^9)](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202411%2Fsimplify3x5y729x10y146x10y1419x10y149x7y9-tjTjs3e4P20t.jpg?x-oss-process=image/resize,w_600,h_600/quality,q_50/format,webp)
Simplify: (3x^5y^-7)^2 (9x^10)/(y^14) (6x^10)/(y^14) (1)/(9x^10)y^(14) 9(x^7)/(y^9)
Solution
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Guilherme
Especialista · Tutor por 3 anos
Resposta
To simplify the expression \(\left(3 x^{5} y^{-7}\right)^{2}\), we need to apply the power of a product rule, which states that \((a \cdot b)^n = a^n \cdot b^n\).Let's break it down:1. Apply the exponent to each part inside the parentheses:
2. Calculate each component: -
- \((x^{5})^2 = x^{10}\) (using the power of a power rule: \((a^m)^n = a^{m \cdot n}\)) - \((y^{-7})^2 = y^{-14}\)3. Combine these results:
Therefore, the simplified form of \(\left(3 x^{5} y^{-7}\right)^{2}\) is
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