Q. Fully simplify using only positive exponents.125x2y65xy6Answer:
Write & Identify Like Terms: Write down the expression and identify like terms.(5xy6)/(125x2y6)We have like terms in the numerator and the denominator that can be simplified.
Simplify Coefficients: Simplify the coefficients (numerical parts) by dividing them. 1255=251
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.For x: x1/x2=x(1−2)=x−1For y: y6/y6=y(6−6)=y0=1 (since any number to the power of 0 is 1)
Combine Coefficients & Variables: Combine the simplified coefficients and variables.(251)×x−1×1Since we want only positive exponents, we need to address the negative exponent.
Convert Negative Exponent: Convert the negative exponent to a positive exponent by taking the reciprocal of the base. x−1=x1
Write Final Simplified Expression: Write the final simplified expression with only positive exponents.(251)×(x1)=25x1
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