Exercise 51 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.

(4.5 \times 1 0^{- 3}) (5.6 \times 1 0^{4})

Remove parentheses

4.5 \times 1 0^{- 3} \times 5.6 \times 1 0^{4}

Commutative Property of Multiplication

4.5 \times 5.6 \times 1 0^{- 3} \times 1 0^{4}

25.2 \times 1 0^{- 3} \times 1 0^{4}

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

25.2 \times 1 0^{- 3 + 4}

Commutative Property of Addition

25.2 \times 1 0^{4 + (- 3)}

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

25.2 \times 1 0^{1}

Note that since

25.2

is not less than

10,

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

25.2

as

2.52 \times 10 .

25.2 \times 1 0^{1}

Rewrite $25.2$ as $2.52 \times 10$

2.52 \times 10 \times 1 0^{1}

$a \cdot a^{m} = a^{1 + m}$

2.52 \times 1 0^{2}

We have written the result of the product in scientific notation. Let's now express it in standard form. Since the exponent is

2,

we need to move the decimal point

2

places to the right.

The result of the product, written in standard form, is $252 .$

Scientific notation : Standard Form : 2.52 \times 1 0^{2} 252