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Fully simplify using only positive exponents. (40x^(7)y^(6))/(16x^(2)y^(7)) Answer:

Fully simplify using only positive exponents.\newline40x7y616x2y7 \frac{40 x^{7} y^{6}}{16 x^{2} y^{7}} \newlineAnswer:

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Q. Fully simplify using only positive exponents.\newline40x7y616x2y7 \frac{40 x^{7} y^{6}}{16 x^{2} y^{7}} \newlineAnswer:
  1. Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.\newlineWe have the coefficient 4040 in the numerator and 1616 in the denominator. We can simplify this by dividing 4040 by 1616.\newlineCalculation: 40÷16=2.540 \div 16 = 2.5
  2. Simplify xx Terms: Simplify the xx terms using the laws of exponents.\newlineWe have x7x^{7} in the numerator and x2x^{2} in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.\newlineCalculation: x7−2=x5x^{7 - 2} = x^{5}
  3. Simplify yy Terms: Simplify the yy terms using the laws of exponents.\newlineWe have y6y^{6} in the numerator and y7y^{7} in the denominator. Again, we subtract the exponents when dividing like bases.\newlineCalculation: y6−7=y−1y^{6 - 7} = y^{-1}
  4. Rewrite with Positive Exponents: Rewrite the expression with only positive exponents.\newlineSince we have y−1y^{-1}, we can rewrite it as 1y\frac{1}{y} to ensure that all exponents are positive.\newlineCalculation: 2.5×x5×(1y)2.5 \times x^{5} \times \left(\frac{1}{y}\right)
  5. Combine Simplified Parts: Combine all the simplified parts to write the final answer.\newlineCalculation: (2.5×x5)/y(2.5 \times x^{5}) / y

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