Question

simplify.
$(2a^{2}b)^{3}$
a. $6a^{5}b^{4}$
b. $6a^{6}b^{3}$
c. $8a^{5}b^{4}$
d. $8a^{6}b^{3}$
e. $8a^{8}b^{3}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So, for \((2a^{2}b)^{3}\), we can apply this rule as follows:
\((2a^{2}b)^{3}=2^{3}\times(a^{2})^{3}\times b^{3}\)

Step2: Simplify each term

• For the coefficient: \(2^{3}=8\)
• For the variable \(a\): Using the power of a power rule \((x^{m})^{n}=x^{m\times n}\), we have \((a^{2})^{3}=a^{2\times3}=a^{6}\)
• For the variable \(b\): \(b^{3}\) remains as it is.

Combining these results, we get \(8\times a^{6}\times b^{3}=8a^{6}b^{3}\)

Answer:

D. \(8a^{6}b^{3}\)