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Multiply and simplify completely, including the elimination of all negati ((3x^(3))/(5y^(8)))^(5)((5^(2)y^(9))/(3^(4)x^(7)))

Multiply and simplify completely, including the elimination of all negati\newline(3x35y8)5(52y934x7) \left(\frac{3 x^{3}}{5 y^{8}}\right)^{5}\left(\frac{5^{2} y^{9}}{3^{4} x^{7}}\right)

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Full solution

Q. Multiply and simplify completely, including the elimination of all negati\newline(3x35y8)5(52y934x7) \left(\frac{3 x^{3}}{5 y^{8}}\right)^{5}\left(\frac{5^{2} y^{9}}{3^{4} x^{7}}\right)
  1. Write Problem: First, let's write down the problem: (3x35y8)5∗(52∗y934∗x7)\left(\frac{3x^3}{5y^8}\right)^5 * \left(\frac{5^2*y^9}{3^4*x^7}\right).
  2. Apply Power: Now, let's apply the power to the first fraction: (35×x3×5)/(55×y8×5)(3^5\times x^{3\times 5})/(5^5\times y^{8\times 5}).
  3. Simplify Powers: Simplify the powers: (243x153125y40)(\frac{243x^{15}}{3125y^{40}}).
  4. Simplify Second Fraction: Next, simplify the second fraction: (25y981x7)(\frac{25y^9}{81x^7}).
  5. Multiply Fractions: Now, multiply the simplified fractions: (243x153125y40)×(25y981x7)(\frac{243x^{15}}{3125y^{40}}) \times (\frac{25y^{9}}{81x^{7}}).
  6. Multiply Numerators and Denominators: Multiply the numerators and denominators: (243×25×x15×y93125×81×y40×x7)(\frac{243\times 25\times x^{15}\times y^{9}}{3125\times 81\times y^{40}\times x^{7}}).
  7. Simplify Multiplication: Simplify the multiplication: (6075x15y9253125y40x7)(\frac{6075x^{15}y^{9}}{253125y^{40}x^{7}}).
  8. Cancel Common Factors: Now, cancel out common factors and subtract the exponents: x(15−7)y(9−40)x^{(15-7)}y^{(9-40)}.
  9. Simplify Exponents: Simplify the exponents: x8y31\frac{x^8}{y^{31}}.
  10. Write Simplified Expression: Finally, write down the simplified expression: x8y31\frac{x^8}{y^{31}}.

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