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Which expression is equivalent to (6x^5z)^3/4x^4z^2?

Option A: 3x^4z^2/2
Option B: 6^4x^11z
Option C: 9x^11z/2
Option D: 6^4x^19z^5

User Naor Bar
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1 Answer

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Final answer:

The expression equivalent to (6x^5z)^3/4x^4z^2 is 9x^11z/2, which we get by cubing the components of the numerator and then dividing by the components of the denominator and simplifying.

Step-by-step explanation:

To find the expression equivalent to (6x^5z)^3 divided by 4x^4z^2, we first simplify the numerator by cubing both the coefficient and the variables. Cubing 6 gives us 216, and the exponent rules indicate that when we raise an exponential term to a power, we multiply the exponents. Therefore, the cubed term becomes 216x^15z^3. Then, we divide this by 4x^4z^2.

Dividing the coefficients, we get 216/4, which is 54. For the variables, we subtract the exponents in the denominator from those in the numerator for the same base, leading to x^(15-4) which is x^11 and z^(3-2) which is z. Hence, the equivalent expression is (54x^11z)/(4x^4z^2), which simplifies further to 9x^11z/2 by dividing both the numerator and denominator by 6.

User Amdg
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