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Fully simplify using only positive exponents.

(18x^(8)y)/(30x^(4)y^(7))
Answer:

Fully simplify using only positive exponents.\newline18x8y30x4y7 \frac{18 x^{8} y}{30 x^{4} y^{7}} \newlineAnswer:

Full solution

Q. Fully simplify using only positive exponents.\newline18x8y30x4y7 \frac{18 x^{8} y}{30 x^{4} y^{7}} \newlineAnswer:
  1. Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.\newlineWe have the coefficients 1818 and 3030. We need to find the greatest common divisor (GCD) of these two numbers to simplify the fraction.\newlineThe GCD of 1818 and 3030 is 66.\newlineSo, we divide both 1818 and 3030 by 66 to simplify the fraction.\newline18÷6=318 \div 6 = 3\newline30÷6=530 \div 6 = 5\newlineNow, the simplified coefficient part is 303000.
  2. Simplify xx Terms: Simplify the xx terms using the laws of exponents.\newlineWe have x8x^{8} in the numerator and x4x^{4} in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.\newlinex8x4=x84=x4\frac{x^{8}}{x^{4}} = x^{8-4} = x^{4}\newlineNow, the xx part is simplified to x4x^{4}.
  3. Simplify y Terms: Simplify the y terms using the laws of exponents.\newlineWe have yy in the numerator and y7y^{7} in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.\newliney/y7=y17=y6y / y^{7} = y^{1-7} = y^{-6}\newlineSince we want only positive exponents, we can write y6y^{-6} as 1/y61/y^{6}.\newlineNow, the y part is simplified to 1/y61/y^{6}.
  4. Combine Simplified Parts: Combine the simplified parts to form the final answer.\newlineWe combine the simplified coefficient (35)(\frac{3}{5}), the simplified xx term (x4)(x^{4}), and the simplified yy term (1y6)(\frac{1}{y^{6}}) to get the final simplified expression.\newlineThe final answer is (35)x4/y6(\frac{3}{5})x^{4}/y^{6}.

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