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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

Chapter Test

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Exercise 12 Page 479

Recall the Property for Dividing Powers with the Same Base.

3* 10^(-6)

Practice makes perfect

We want to simplify the given quotient and express it in scientific notation. To do so, we will apply the Property for Dividing Powers With the Same Base. a^m/a^n = a^(m-n)The above property is valid when a≠ 0 and when m and n are both rational numbers. Let's do it!

1.5* 10^(- 7)/5* 10^(- 2)

Write as a product of fractions

1.5/5 * 10^(- 7)/10^(- 2)

a^m/a^n= a^(m-n)

1.5/5 * 10^(- 7-(- 2))

a-(- b)=a+b

1.5/5 * 10^(- 7+2)

Add terms

1.5/5 * 10^(- 5)

Calculate quotient

0.3* 10^(- 5)

Now we have to write the simplified expression in scientific notation.

0.3* 10^(- 5)

Rewrite 0.3 as 3* 10^(- 1)

3 * 10^(- 1) * 10^(- 5)

a^(m+n)=a^m*a^n

3 * 10^(- 1 + (- 5))

a+(- b)=a-b

3 * 10^(- 1 - 5)

Subtract term

3 * 10^(- 6)

Note that we do not want to continue multiplying or simplifying, because the simplified expression is now written in proper scientific notation.