Step 1: Begin by applying the power of a power property to the numerator. This property states that when you raise a power to a power, you multiply the exponents. We can raise each term in the base (inside the parentheses) to the power outside the parentheses:
Therefore, the numerator is simplified to:
(6^3 * x^(3 * (2/7)) * y^(3 * (-4)) * z^(3 * 0))
Step 2: Simplify the resulting equation:
Hence, the numerator simplifies to:
216 * x^(6/7) * y^-12 * z^0
Step 3: Begin simplifying the denominator by writing each term with positive exponents only. Use the property of exponents that state: when you divide terms with the same base, you subtract the exponents.
Thus, the denominator simplifies to:
9 * x^2 * y^5 * z^8
Step 4: As you notice the numerator and denominator have several terms with the same base (x, y, and z), apply the property of division for the exponents. Divide the terms in the numerator by the corresponding terms in the denominator in order to subtract their exponents:
As a result, the algebraic expression simplifies to:
(216 / 9) * x^((6/7) - 2) * y^(-12 - 5) * z^(0 - (-8))
Step 5: Simplify the expression further:
Which simplifies to:
24 * x^(-8/7) * y^-17 * z^8
Step 6: Write the answer with no variable in the denominator. To do this, remember that a negative exponent means the term is on the wrong side of the fraction bar. Therefore, a base with a negative exponent will change sides (from top to bottom or bottom to top).
Final answer:
24 * z^8 / (x^(8/7) * y^17)
This equates to:
24 * z^8 / (x^1.14 * y^17)
And that is your simplified expression with no variable at the denominator.