Evaluate ((4.5)(10^-2)3.210^-1)/((1)(10^4)4.010^-4)

$\frac{(4.5) (10^{- 2}) \cdot 3.2 \cdot 10^{- 1}}{(1) (10^{4}) \cdot 4 \cdot 10^{- 4}}$

Step 1

Multiply $10^{- 2}$ by $10^{- 1}$ by adding the exponents.

Move $10^{- 1}$ .

$\frac{4.5 (10^{- 1} \cdot 10^{- 2}) \cdot 3.2}{(1) (10^{4}) \cdot 4 \cdot 10^{- 4}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4.5 \cdot 10^{- 1 - 2} \cdot 3.2}{(1) (10^{4}) \cdot 4 \cdot 10^{- 4}}$

Subtract $2$ from $- 1$ .

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{(1) (10^{4}) \cdot 4 \cdot 10^{- 4}}$

Step 2

Multiply $10^{4}$ by $1$ .

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{10^{4} \cdot 4 \cdot 10^{- 4}}$

Step 3

Multiply $10^{4}$ by $10^{- 4}$ by adding the exponents.

Move $10^{- 4}$ .

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{10^{- 4} \cdot 10^{4} \cdot 4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{10^{- 4 + 4} \cdot 4}$

Add $- 4$ and $4$ .

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{10^{0} \cdot 4}$

Step 4

Simplify.

Simplify $10^{0} \cdot 4$ .

$\frac{4.5 \cdot 10^{- 3} \cdot 3.2}{4}$

Move $10^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4.5 \cdot 3.2}{4 \cdot 10^{3}}$

Step 5

Multiply $4.5$ by $3.2$ .

$\frac{14.4}{4 \cdot 10^{3}}$

Step 6

Divide using scientific notation.

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{14.4}{4}) (\frac{1}{10^{3}})$

Divide $14.4$ by $4$ .

$3.6 \frac{1}{10^{3}}$

Move $10^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3.6 \cdot 10^{- 3}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$3.6 \cdot 10^{- 3}$

Expanded Form:

$0.0036$

Evaluate ((4.5)(10^-2)*3.2*10^-1)/((1)(10^4)*4.0*10^-4)