Question

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2

Format your answer like this: The result of the scientific notation is __*10^--. The result as a decimal is _.

Answer 1

• the result in scientific notation is 6.561×10⁻⁷
• the result as a decimal is 0.000 000 656 1

Step-by-step explanation:

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561