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(18x^(7)y^(4))/(12x^(9)y^(4))

18x7y412x9y4 \frac{18 x^{7} y^{4}}{12 x^{9} y^{4}}

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Full solution

Q. 18x7y412x9y4 \frac{18 x^{7} y^{4}}{12 x^{9} y^{4}}
  1. Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.\newlineDivide 1818 by 1212 to simplify the coefficients.\newline18/12=1.518 / 12 = 1.5 or 32\frac{3}{2}
  2. Simplify xx Terms: Simplify the xx terms by using the property of exponents xaxb=xa−b\frac{x^a}{x^b} = x^{a-b}.\newlineSubtract the exponents of xx.\newline7−4=37 - 4 = 3\newlineSo, x7−4=x3x^{7-4} = x^3
  3. Simplify yy Terms: Simplify the yy terms by using the property of exponents yayb=ya−b\frac{y^a}{y^b} = y^{a-b}. Since the exponents of yy are the same, y4−4=y0y^{4-4} = y^0. Any number to the power of 00 is 11, so y0=1y^0 = 1.
  4. Combine Results: Combine the results from Step 11, Step 22, and Step 33.\newlineThe simplified expression is (32)x3×1(\frac{3}{2})x^3 \times 1, which is just (32)x3(\frac{3}{2})x^3.

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