Exercise 52 Page 429

We want to evaluate the product. To do so, we will use the Commutative Property of Multiplication and the Product of Powers Property.

(3.8 \times 1 0^{- 4}) (6.4 \times 1 0^{- 8})

Remove parentheses

3.8 \times 1 0^{- 4} \times 6.4 \times 1 0^{- 8}

Commutative Property of Multiplication

3.8 \times 6.4 \times 1 0^{- 4} \times 1 0^{- 8}

24.32 \times 1 0^{- 4} \times 1 0^{- 8}

$a^{m} \cdot a^{n} = a^{m + n}$

24.32 \times 1 0^{- 4 + (- 8)}

$a + (- b) = a - b$

24.32 \times 1 0^{- 4 - 8}

Subtract term

24.32 \times 1 0^{- 12}

Note that since

24.32

is not less than

10,

the above number is not written in scientific notation. We can fix this by rewriting

24.32

as

2.432 \times 10 .