Question

simplify ((3n^2n^4)^3)
a ((3n^6)^3)
o (3n^{18})
u no error
choose

Explanation:

Step1: Simplify inside the parentheses

First, we simplify the exponents of \( n \) inside the parentheses. When multiplying variables with exponents, we add the exponents: \( n^{2} \cdot n^{4}=n^{2 + 4}=n^{6} \). So the expression inside the parentheses becomes \( 3n^{6} \), which is step A, so step A is correct.

Step2: Apply the power of a power rule

Now we apply the exponent 3 to both the coefficient and the variable. The power of a power rule states that \( (a^{m})^{n}=a^{m\times n} \) and \( (ab)^{n}=a^{n}b^{n} \). So for \( (3n^{6})^{3} \), we have \( 3^{3}\times(n^{6})^{3} \). Calculating \( 3^{3}=27 \) and \( (n^{6})^{3}=n^{6\times3}=n^{18} \). So the correct simplification should be \( 27n^{18} \), but the step shown as O (probably a typo, maybe "B" or another label) has \( 3n^{18} \), which is incorrect because the coefficient 3 was not raised to the power of 3. So the error occurs in the step with \( 3n^{18} \), but since we are to choose the step where the error occurred or U for no error, and step A is correct, the error is in the step after A (the one with \( 3n^{18} \)). But looking at the options, the options are A, O (with \( 3n^{18} \)), U. Since step A is correct, and the next step (O) is wrong, the error is in the step labeled O (the one with \( 3n^{18} \)). But if we consider the options given, the error is in the step that has \( 3n^{18} \) (the O step), so the error occurs there, so the answer is the step with \( 3n^{18} \) (the O option), meaning the error is in that step, so we choose that step (but the problem says "choose the letter U for no error" or the step with error. Since step A is correct, and the next step (O) is wrong, the error is in O. But let's re - check:

Original expression: \( (3n^{2}n^{4})^{3} \)

Step 1 (A): \( (3n^{6})^{3} \) (correct, since \( n^{2}\cdot n^{4}=n^{6} \))

Step 2 (the O step): \( 3n^{18} \) (incorrect, because \( (3n^{6})^{3}=3^{3}\times(n^{6})^{3}=27n^{18} \), not \( 3n^{18} \))

So the error is in the step labeled O (the one with \( 3n^{18} \)), so we choose that step (the option with \( 3n^{18} \), which is labeled O, but in the options given, the error is in that step, so the answer is the step with \( 3n^{18} \) (the O option), meaning the error occurs there, so we select that step (the O option). But if we have to choose between A, O, U, since A is correct and O is wrong, the error is in O.

Answer:

The step with the error is the one labeled O (the step with \( 3n^{18} \)), so the answer is the option with \( 3n^{18} \) (assuming O is the label for that step, so we choose the option with \( 3n^{18} \), which is the incorrect step).