Question

In the expression (5x^6)(3x^3)^4, what is the value of xt?

A) xt = 72

B) xt = 54

C) xt = 27

D) xt = 108

Answer 1

The question is unclear as it asks for the value of 'xt', which is not defined in the given mathematical expression. Assuming the intent is to simplify the expression, the result would be 405x^18. The variable 'xt' is not computable from the information provided.

Step-by-step explanation:

The expression given is (5x^6)(3x^3)^4, and the question seems to be asking for the value of a variable xt. However, xt is not defined in the context of the mathematical expression, suggesting there might be a misunderstanding or typo in the question. Assuming the question intends to find the result of the given expression:

First, apply the exponent to the term inside the parentheses: (3x^3)^4. According to the rules for cubing of exponentials, you cube the digit term and multiply the exponential term by 3, which gives 81x^{12} (since 3^4 is 81 and 3*4 is 12).

Then, multiply this with the other term outside the parentheses: 5x^6. When multiplying exponential terms with the same base, you add the exponents: 5x^6 * 81x^{12} = 405x^{18}.

This final expression represents the outcome of the given operation, but it does not provide a numerical value for xt as that is not a variable defined or calculable from the given expression.