Question 18 What is the following expression equivalent to? \[ \left(b^{3}\right)^{4} b^{5} \]

Step 1 ：The given expression is \((b^{3})^{4} b^{5}\).

Step 2 ：We can simplify this expression by using the properties of exponents.

Step 3 ：The rule of exponents states that when you raise a power to a power, you multiply the exponents. So, \((b^{3})^{4}\) can be simplified to \(b^{3*4}\) or \(b^{12}\).

Step 4 ：Then, we have \(b^{12} * b^{5}\).

Step 5 ：The rule of exponents also states that when you multiply like bases, you add the exponents. So, \(b^{12} * b^{5}\) can be simplified to \(b^{12+5}\) or \(b^{17}\).

Step 6 ：So, the given expression is equivalent to \(b^{17}\).

Step 7 ：Final Answer: The given expression is equivalent to \(\boxed{b^{17}}\).