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Fully simplify using only positive exponents.

(5xy^(6))/(125x^(2)y^(6))
Answer:

Fully simplify using only positive exponents.\newline5xy6125x2y6 \frac{5 x y^{6}}{125 x^{2} y^{6}} \newlineAnswer:

Full solution

Q. Fully simplify using only positive exponents.\newline5xy6125x2y6 \frac{5 x y^{6}}{125 x^{2} y^{6}} \newlineAnswer:
  1. Write & Identify Like Terms: Write down the expression and identify like terms.\newline(5xy6)/(125x2y6)(5xy^6) / (125x^2y^6)\newlineWe have like terms in the numerator and the denominator that can be simplified.
  2. Simplify Coefficients: Simplify the coefficients (numerical parts) by dividing them. 5125=125\frac{5}{125} = \frac{1}{25}
  3. Simplify Variables with Exponents: Simplify the variables with exponents by subtracting the exponents of like bases in the denominator from the exponents of like bases in the numerator.\newlineFor xx: x1/x2=x(12)=x1x^1 / x^2 = x^{(1-2)} = x^{-1}\newlineFor yy: y6/y6=y(66)=y0=1y^6 / y^6 = y^{(6-6)} = y^0 = 1 (since any number to the power of 00 is 11)
  4. Combine Coefficients & Variables: Combine the simplified coefficients and variables.\newline(125)×x1×1(\frac{1}{25}) \times x^{-1} \times 1\newlineSince we want only positive exponents, we need to address the negative exponent.
  5. Convert Negative Exponent: Convert the negative exponent to a positive exponent by taking the reciprocal of the base. x1=1xx^{-1} = \frac{1}{x}
  6. Write Final Simplified Expression: Write the final simplified expression with only positive exponents.\newline(125)×(1x)=125x(\frac{1}{25}) \times (\frac{1}{x}) = \frac{1}{25x}

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