Evaluate Using Scientific Notation ((5.210^7)(510^8))/((3.210^6)(510^5))

$\frac{(5.2 \cdot 10^{7}) (5 \cdot 10^{8})}{(3.2 \cdot 10^{6}) (5 \cdot 10^{5})}$

Step 1

Multiply $5.2$ by $5$ .

$\frac{26 (10^{7} \cdot 10^{8})}{(3.2 \cdot 10^{6}) (5 \cdot 10^{5})}$

Step 2

Multiply $10^{7}$ by $10^{8}$ by adding the exponents.

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

$\frac{26 \cdot 10^{7 + 8}}{(3.2 \cdot 10^{6}) (5 \cdot 10^{5})}$

Add $7$ and $8$ .

$\frac{26 \cdot 10^{15}}{(3.2 \cdot 10^{6}) (5 \cdot 10^{5})}$

Step 3

Multiply $3.2$ by $5$ .

$\frac{26 \cdot 10^{15}}{16 (10^{6} \cdot 10^{5})}$

Step 4

Multiply $10^{6}$ by $10^{5}$ by adding the exponents.

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

$\frac{26 \cdot 10^{15}}{16 \cdot 10^{6 + 5}}$

Add $6$ and $5$ .

$\frac{26 \cdot 10^{15}}{16 \cdot 10^{11}}$

Step 5

Divide using scientific notation.

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

$(\frac{26}{16}) (\frac{10^{15}}{10^{11}})$

Divide $26$ by $16$ .

$1.625 \frac{10^{15}}{10^{11}}$

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$1.625 \cdot 10^{15 + 11 \cdot - 1}$

Multiply $11$ by $- 1$ .

$1.625 \cdot 10^{15 - 11}$

Subtract $11$ from $15$ .

$1.625 \cdot 10^{4}$

Evaluate Using Scientific Notation ((5.2*10^7)(5*10^8))/((3.2*10^6)(5*10^5))