Question

structure determine whether the pair of expressions is equivalent. select yes or no. ((6w^{3})^{3}) and (36w^{18})
select choice
select choice
yes
no

Explanation:

Step1: Expand the first expression

Apply exponent rules: $(ab^n)^m = a^m b^{n \cdot m}$
$$(6w^4)^2 = 6^2 \cdot w^{4 \cdot 2}$$

Step2: Calculate each component

Compute the numerical and variable terms:
$$6^2 = 36, \quad w^{4 \cdot 2} = w^8$$

Step3: Compare the two expressions

The expanded first expression is $36w^8$, which does not match $36w^{16}$.

Answer:

no