Evaluate Using Scientific Notation (510^4610^-3)/(310^-5110^2)

$\frac{5 \cdot 10^{4} \cdot 6 \cdot 10^{- 3}}{3 \cdot 10^{- 5} \cdot 1 \cdot 10^{2}}$

Step 1

Multiply $5$ by $6$ .

$\frac{30 (10^{4} \cdot 10^{- 3})}{3 \cdot 10^{- 5} \cdot 1 \cdot 10^{2}}$

Step 2

Multiply $10^{4}$ by $10^{- 3}$ by adding the exponents.

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

$\frac{30 \cdot 10^{4 - 3}}{3 \cdot 10^{- 5} \cdot 1 \cdot 10^{2}}$

Subtract $3$ from $4$ .

$\frac{30 \cdot 10^{1}}{3 \cdot 10^{- 5} \cdot 1 \cdot 10^{2}}$

Step 3

Simplify $10^{1}$ .

$\frac{30 \cdot 10}{3 \cdot 10^{- 5} \cdot 1 \cdot 10^{2}}$

Step 4

Multiply $3$ by $1$ .

$\frac{30 \cdot 10}{3 (10^{- 5} \cdot 10^{2})}$

Step 5

Multiply $10^{- 5}$ by $10^{2}$ by adding the exponents.

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

$\frac{30 \cdot 10}{3 \cdot 10^{- 5 + 2}}$

Add $- 5$ and $2$ .

$\frac{30 \cdot 10}{3 \cdot 10^{- 3}}$

Step 6

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

$\frac{30 \cdot 10 \cdot 10^{3}}{3}$

Step 7

Multiply $10$ by $10^{3}$ by adding the exponents.

Move $10^{3}$ .

$\frac{30 \cdot (10^{3} \cdot 10)}{3}$

Multiply $10^{3}$ by $10$ .

Raise $10$ to the power of $1$ .

$\frac{30 \cdot (10^{3} \cdot 10^{1})}{3}$

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

$\frac{30 \cdot 10^{3 + 1}}{3}$

Add $3$ and $1$ .

$\frac{30 \cdot 10^{4}}{3}$

Step 8

Divide using scientific notation.

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

$(\frac{30}{3}) (\frac{10^{4}}{1})$

Divide $30$ by $3$ .

$10 \frac{10^{4}}{1}$

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

$10 \cdot 10^{4}$

Step 9

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

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

Raise $10$ to the power of $1$ .

$10^{1} \cdot 10^{4}$

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

$10^{1 + 4}$

Add $1$ and $4$ .

$10^{5}$

Step 10

Raise $10$ to the power of $5$ .

$100000$

Evaluate Using Scientific Notation (5*10^4*6*10^-3)/(3*10^-5*1*10^2)

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Evaluate Using Scientific Notation (510^4610^-3)/(310^-5110^2)