Problem 56 - Algebra A Combined Function

Question

Perform the indicated operation. \((-0.3)^{3}\)

Step-by-Step Solution

Answer

The result is \(-0.027\).

Step 1: Understand the Expression

The given expression is \((-0.3)^3\). This means we are raising the number \(-0.3\) to the third power, i.e., we need to multiply \(-0.3\) by itself three times.

Step 2: Multiply the Base

Start by multiplying \(-0.3\) by itself: \((-0.3) \times (-0.3) = 0.09\). Multiplying two negative numbers results in a positive product.

Step 3: Raise to the Third Power

Now, multiply the result from Step 2 by \(-0.3\) again: \(0.09 \times (-0.3) = -0.027\). Multiplying a positive number by a negative number results in a negative product.

Key Concepts

Negative Numbers

Negative numbers can be a bit confusing at first, but they are essentially just numbers with values less than zero. You can think of them as numbers that are to the left of zero on the number line. Negative numbers are commonly used in everyday situations, such as to denote temperatures below freezing or financial losses.

When dealing with operations involving negative numbers, there are some important rules to remember:

• When you multiply two negative numbers, the result is a positive number.
• If you multiply a positive number by a negative number (or vice versa), the result is a negative number.
• Subtracting a negative number is the same as adding the corresponding positive number.

Understanding these rules can help you tackle exercises involving negative numbers with greater confidence.

Multiplication

The operation of multiplication involves combining equal groups. For example, if you multiply 3 by 4, it means you are adding the number 3 a total of 4 times: 3 + 3 + 3 + 3, which equals 12. In the context of the problem equation: equation: (-0.3)^3, we are essentially finding the product of with itself three times, multiplying step by step. Some key points about multiplication include:

• The order of numbers in multiplication does not affect the result (i.e., multiplication is commutative): 3 × 4 = 4 × 3.
• Multiplying by zero always gives a result of zero.
• Multiplying by one leaves the number unchanged.

By knowing these basic rules, you'll find it easier to perform multiplication in more complex mathematical operations, including those with negative numbers or exponents.

Powers of Numbers

Raising a number to a power means multiplying it by itself a certain number of times indicated by the exponent. In the expression (-0.3)^3, the number -0.3 is the base and 3 is the exponent. This tells us to multiply -0.3 by itself three times. When we deal with powers of numbers, we need to understand:

• If the base is negative and the exponent is odd, the final result is negative.
• If the base is negative and the exponent is even, the final result is positive.
• Raising any number to the power of one results in the number itself.

Applying these rules, we can determine our expression results in (-0.3) and minus results, allowing you to approach calculations more systematically.