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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

3. More Multiplication Properties of Exponents

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Exercise 39 Page 437

Recall the Power of a Product and the Power of a Power Properties.

2.56* 10^(22)

Practice makes perfect

We want to simplify the given expression and write the answer in scientific notation. To do so, we will apply the Power of a Product and the Power of a Power Properties. Power of a Product:& (ab)^n = a^nb^n Power of a Power:& (a^m)^n = a^(m* n)The above properties are valid when a≠ 0, b≠ 0, and when m and n are any rational numbers. Let's do it!

( 6.25* 10^(- 12) )^(-2)

(a * b)^m=a^m* b^m

6.25^(-2) * ( 10^(- 12) )^(-2)

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

(6.25)^(-2) * 10^(24)

NegExponentToFrac

a^(- m)=1/a^m

1/(6.25)^2 * 10^(24)

Calculate power

1/39.0625 * 10^(24)

Calculate quotient

0.0256* 10^(24)

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

0.0256* 10^(24)

Rewrite 0.0256 as 2.56* 10^(-2)

2.56* 10^(-2) * 10^(24)

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

2.56* 10^(-2+24)

Add terms

2.56* 10^(22)

Subchapter links

Lesson Check p.436

Practice and Problem-Solving Exercises p.436-438

Standardized Test Prep p.438

Mixed Review p.438