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Multiplication is one of the basic arithmetic operations. It involves adding a number (called the multiplicand) to itself a certain number of times (specified by another number called the multiplier). For example, multiplying 2 by 3 means adding 2 three times: 2 + 2 + 2.

When dealing with decimal numbers, the same principles apply. However, attention to detail is crucial because each number involved has a place value. To multiply decimal numbers, you can temporarily ignore the decimals and multiply as if working with whole numbers.

Decimal numbers are numbers that have a whole number part and a fractional part separated by a decimal point. For instance, the number 0.3 means 3 tenths or 3/10.

When multiplying decimals, it’s vital to count the total number of decimal places in both factors. After performing the multiplication as if they were whole numbers, you return the decimal point to the correct place in the product by ensuring the number of decimal places in the result matches the total from the factors.

In the given exercise, you multiply 0.3 by itself three times. To do this, first multiply 0.3 by 0.3 to get 0.09 (since 3x3 is 9 and there are two decimal places in total). Then, you multiply 0.09 by 0.3, resulting in 0.027 (since 9x3 is 27 and there are three decimal places in total).

Exponents are a way to express repeated multiplication of the same number. An exponent is written as a small number above and to the right of the base number. For example, in the expression \(3^2\), 3 is the base and 2 is the exponent, meaning 3 is multiplied by itself 2 times: \(3 \times 3 = 9\).

In this exercise, we have the expression \( (0.3)^3 \), which means multiplying 0.3 by itself three times: \(0.3 \times 0.3 \times 0.3\).

This notation is a shorthand that makes it easier to write and interpret repeated multiplication. Applying this to our problem, we multiply as follows:

• First: \(0.3 \times 0.3\) resulting in 0.09.
• Then: \(0.09 \times 0.3\) resulting in 0.027.

Therefore, \( (0.3)^3 \) equals 0.027.