Final answer:
To remove the denominator from the expression 3a²b³c⁵/8x⁴y³z, apply the Division of Exponentials by inverting the denominator's terms to the numerator with negative exponents, resulting in the simplified form 3a²b³c⁵x⁻⁴y⁻³z⁻¹.
Step-by-step explanation:
To rewrite the expression 3a²b³c⁵/8x⁴y³z so that it has no denominator, we can use the concept of Division of Exponentials. This involves dividing the digit term of the numerator by the digit term of the denominator and subtracting the exponents of the exponential terms for each of the variables involved.
The process of removing the denominator also involves moving the denominator terms to the numerator and assigning negative exponents to them. Therefore, the expression without a denominator becomes 3a²b³c⁵x⁻⁴y⁻³z⁻¹.
In other words, you simply invert the terms of the denominator and place them in the numerator with negative exponents. This approach leverages the rules of exponents, which state that a term with a negative exponent in the numerator is equivalent to the term with a positive exponent in the denominator, effectively allowing the original denominator to be 'canceled out'.