Exercise 18 Page 72

Practice makes perfect

We want to find the value of n in the given equation. 1.5 * 10^(12) = (5 * 10^5)(3 * 10^n) To do it, let's simplify the multiplication on the right-hand side. Then we will compare it to the left-hand side of the given equation.

( 5 * 10^5)( 3 * 10^n)

CommutativePropMult

Commutative Property of Multiplication

( 5 * 3 ) * ( 10^5 * 10^n)

Multiply

15 * 10^5 * 10^n

MultPow

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

15 * 10^(5+n)

Notice that 15 is not less than 10. Therefore, to rewrite this expression in scientific notation, we will rewrite 15 as 1.5 * 10.

15 * 10^(5+n)

Rewrite

Rewrite 15 as 1.5 * 10

1.5 * 10 * 10^(5+n)

a=a^1

1.5 * 10^1 * 10^(5+n)

MultPow

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

1.5 * 10^(1+5+n)

AddTerms

Add terms

1.5 * 10^(6+n)

We found that the right-hand side of the given equation simplifies to 1.5 * 10^(6+n). Now we can compare the left-hand side with the right-hand side. 1.5 * 10^(12) = 1.5 * 10^(6+n) Notice that for the left-hand side to be equal to the right-hand side, we need 6+n to be equal to 12. 6+n = 12 ⇔ n = 6 We found that the value of n in the given equation is 6.

We are asked to explain why the exponent on the left side of the equation is not equal to the sum of the exponents on the right side of the given equation. In Part A we found that the value of n is 6.

1.5 * 10^(12) = (5 * 10^5)(3 * 10^6) The exponent on the left-hand side is 12. We can see that the sum of the exponents on the right-hand side of the given equation is 11. 5 + 6 = 11 After multiplying the factors on the right-hand side of the given equation with n, we got 15 * 10^(5+n). To rewrite it in scientific notation, we had to rewrite 15 as 1.5 * 10, which changed the value of the exponent to 6+n. That is why the exponent on the left side is not equal to the sum of the exponents on the right side.

Subchapter links

Do You Understand? p.70

Do You Know How? p.70

Practice & Problem Solving p.71-72

Assessment Practice p.72

Exercise 18 Page 72

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