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By John P Hutchison; Neil Skinner

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Each water molecule contains 3 atoms (2 hydrogen and 1 oxygen). 22 × 104 average drops. 83 × 1025 atoms in 1 L of water. We simply multiply the decimal terms and add the exponents. Imagine having to perform the calculation without using scientific notation! When performing calculations with scientific notation, be sure to write the answer in proper scientific notation. For example, consider the product (7 × 104) × (5 × 106) = 35 × 1010. The answer is not in proper scientific notation because 35 is greater than 10.

Simplify exponential expressions. • Use scientific notation. 1. 2 EXPONENTS AND SCIENTIFIC NOTATION Mathematicians, scientists, and economists commonly encounter very large and very small numbers. But it may not be obvious how common such figures are in everyday life. For instance, a pixel is the smallest unit of light that can be perceived and recorded by a digital camera. A particular camera might record an image that is 2,048 pixels by 1,536 pixels, which is a very high resolution picture.

Do not simplify further.  ((−g)4)4 Using the Zero Exponent Rule of Exponents Return to the quotient rule. We made the condition that m > n so that the difference m − n would never be zero or negative. What would happen if m = n? In this case, we would use the zero exponent rule of exponents to simplify the expression to 1. To see how this is done, let us begin with an example. t 8 t ​ 8 ​ ​ __8 ​ = ​ __8 ​ = 1 t t​ ​ If we were to simplify the original expression using the quotient rule, we would have t 8 ​ __8 ​ = t 8 − 8 = t 0 t If we equate the two answers, the result is t0 = 1.

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