Problem 52 - Algebra 1

Question

Use a calculator to evaluate the expression. Round your answer to two decimal places. $$(3.6)(-2.67)^{3}(-9.41)$$

Step-by-Step Solution

Answer

After performing the calculation and rounding to two decimal places, the final result is 644.03.

Step 1: Identify the operation

The operation in question is (3.6)(-2.67)^{3}(-9.41). It includes multiplication and exponentiation.

Step 2: Apply exponentiation first

According to BIDMAS rule, perform operations with exponentiation first. So, calculate (-2.67) cubed. Since cube of a negative number is also a negative number, (-2.67)^3 equals -19.089763. Note that you should keep more decimal places at this intermediate step to keep the final answer accurate.

Step 3: Then, conduct multiplication

Next, again following the BIDMAS rule, perform multiplication. Multiply 3.6, -19.089763, and -9.41. The result of the calculation is 644.026163776

Step 4: Round the answer

Finally, round your answer to two decimal places. This operation gets a final result of 644.03.

Key Concepts

Exponentiation

Exponentiation is a mathematical operation that involves raising a number to a specific power. In simple terms, it means multiplying the number by itself a certain number of times. For example, when you see "\((-2.67)^3\)," it means you are raising

• -2.67 to the power of 3.
• This involves multiplying -2.67 by itself twice more: \((-2.67) \times (-2.67) \times (-2.67)\).
• In this case, since multiplying two negative numbers results in a positive number and multiplying a positive number with a negative number gives a negative number, the result remains negative.
• The operation results in approximately -19.089763.

Rounding this intermediate result to more decimal places helps in maintaining precision till the final result calculation. Practicing exponentiation helps sharpen your skills in solving both simple and complex mathematical problems. Always remember when dealing with negative numbers and exponents that the sign of the result will alternate depending on whether the power is odd or even.

Multiplication

Multiplication is a basic arithmetic operation that combines one number with another to produce a product. It's essential to grasp this concept because it's foundational in mathematics. In the context of the exercise, after the exponentiation process is complete, the next step is multiplication.

• You take the result from the exponentiation, which gives you \(-19.089763\), and multiply it by 3.6 and -9.41.
• Following the order: \(3.6 \times (-19.089763) \times (-9.41)\).

This step highlights the importance of understanding how positive and negative numbers interact:

• Multiplying a negative number (from the exponentiation) with a positive number (3.6) results in a negative product.
• Further, multiplying two negative numbers (-19.089763 and -9.41) translates into a positive product.

The resulting product from this multiplication process is approximately 644.026163776, and understanding these interactions helps ensure accuracy in your calculations.

BIDMAS

BIDMAS is an acronym that helps students remember the correct order of operations in mathematical expressions. It stands for Brackets, Indices (another word for exponents), Division and Multiplication (from left to right), Addition, and Subtraction (from left to right).Understanding BIDMAS is crucial because it dictates the order in which operations should be performed to correctly evaluate expressions. In the provided exercise, BIDMAS guides us to:

• First, look at any parts of the expression that need exponentiation. In this case, the index operation is \((-2.67)^3\).
• Next, we perform multiplication. Here, this means multiplying the result of the exponentiation (\(-19.089763\)) with 3.6 and -9.41.

By following this sequence, you ensure that your calculations are done systematically and correctly. Rounding to two decimal places at the final step provides a neat and accurate result. Having a firm grip on BIDMAS allows you not only to work accurately with everyday math problems but also to tackle more complex mathematical equations smoothly. Always keep BIDMAS in mind when solving expressions to avoid errors and mix-ups.