Question

Write your answer as a power or as a product of powers. $$ \left[(2 x+3)^{3}\right]^{2} $$

Short answer

\( (2x+3)^6 \)

Step-by-step solution

Identify the Base and Exponents

Firstly, identify the base and the exponents. The base is \(2x+3\), the first exponent is 3, and the second exponent is 2.

Apply the Power of a Power Rule

Apply the power of a power rule, which states that \( (a^m)^n = a^{m*n} \). Here, \(a\) is \(2x+3\), \(m\) is 3, and \(n\) is 2. Multiplying the exponents 3 and 2 together gives 6.

Write the Result

The result will be the base \(2x+3\) raised to the power of the product of exponents, which is 6. Therefore, the final answer would be \( (2x+3)^6 \).