Question

Use a is calculator to evaluate the expression. Round the result to two decimal places when appropriate. $$\left(2.9^{3}\right)^{5}$$

Short answer

The evaluation of the given expression rounded to two decimal places is 7599809161.20.

Step-by-step solution

Understand the order of operations

In mathematics, there is a specific order in which operations should be performed to get the right answer. This is typically remembered using the acronym BIDMAS or PEMDAS, which stands for Brackets/Parentheses, Indices/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). Using this rule, one should start by solving the expression inside the parentheses first.

Evaluate the expression inside the parentheses

Inside the parentheses, the expression is \(2.9^{3}\). This means 2.9 should be multiplied by itself three times. Using a calculator, one can find this value equals 24.389.

Evaluate the whole expression

With the value from the parentheses now known, substitute this back into the original expression to get \((24.389)^{5}\). Once again, this means 24.389 should be multiplied by itself five times. Using a calculator, this evaluates to roughly 7599809161.2.

Round Result

The prompt asks to round the result to two decimal places if appropriate. So, the final result of the expression is rounded to become 7599809161.20.