What action should be taken when performing operations with powers of ten in standard form?

What action should be taken when performing operations with powers of ten in standard form?

• A. Multiply the powers whenever necessary
• B. Add them directly to a constant
• C. Combine them through multiplication or division
• D. Convert them to fractions

Answer: (C)

When working with powers of ten in standard form, combining them through multiplication or division is the correct approach. This is because standard form typically expresses numbers as a product of a coefficient and a power of ten, such as \( a \times 10^n \), where \( a \) is a number between 1 and 10, and \( n \) is an integer. For example, when multiplying two numbers in standard form, you would multiply the coefficients (the numbers in front) and then add the exponents of the powers of ten. Similarly, when dividing, you would divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator. This systematic approach ensures that calculations remain consistent with the properties of exponents, resulting in the correct standard form as your final answer. In contrast, other approaches such as merely adding numbers directly to a constant or converting them to fractions do not maintain the integrity of the standard form representation and would not yield correct results according to the rules of manipulating powers of ten.

When working with powers of ten in standard form, combining them through multiplication or division is the correct approach. This is because standard form typically expresses numbers as a product of a coefficient and a power of ten, such as ( a \times 10^n ), where ( a ) is a number between 1 and 10, and ( n ) is an integer.

For example, when multiplying two numbers in standard form, you would multiply the coefficients (the numbers in front) and then add the exponents of the powers of ten. Similarly, when dividing, you would divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator. This systematic approach ensures that calculations remain consistent with the properties of exponents, resulting in the correct standard form as your final answer.

In contrast, other approaches such as merely adding numbers directly to a constant or converting them to fractions do not maintain the integrity of the standard form representation and would not yield correct results according to the rules of manipulating powers of ten.