Question

Write your answer as a power or as a product of powers. $$ 2 x^{3} \cdot(3 x)^{2} $$

Short answer

The simplified expression is \(18x^5\)

Step-by-step solution

Observe the given expression

Look at the given expression \(2 x^{3} \cdot(3 x)^{2}\). Observe that it is a product of two terms: \(2 x^{3}\) and \((3 x)^{2}\).

Apply the power of a power rule

The second term \((3 x)^{2}\) includes a power of a power. This can be simplified using the rule \((a^m)^n = a^{m*n}\). This gives \((3 x)^{2} = 3^2 \cdot x^{2} = 9x^{2}\)

Combine the terms

Now, replace \((3 x)^{2}\) in the initial expression with the result obtained in Step 2. Therefore, the expression becomes \(2 x^{3} \cdot 9x^{2}\). Using the rule for multiplying powers with the same base, we add the exponents and obtain \(2 \cdot 9 x^{3+2} = 18x^5\)