Question

simplify the expression \\(\left(\left(-2w\
ight)^2\
ight)^3\\)
options: (64w^5), (-64w^6), (64w^6), (-64w^5)

Explanation:

Step1: Apply power of a power rule

For \((( - 2w)^{2})^{3}\), use the rule \((a^{m})^{n}=a^{mn}\). First, simplify the inner exponent: \((-2w)^{2}=(-2)^{2}\times w^{2}=4w^{2}\) (since squaring a negative gives a positive).

Step2: Apply power of a power again

Now we have \((4w^{2})^{3}\). Using the rule \((ab)^{n}=a^{n}b^{n}\) and \((a^{m})^{n}=a^{mn}\), we get \(4^{3}\times(w^{2})^{3}\). Calculate \(4^{3}=64\) and \((w^{2})^{3}=w^{2\times3}=w^{6}\). So the simplified expression is \(64w^{6}\).

Answer:

64w⁶ (corresponding to the option "64w⁶" among the choices)