Basic Math Examples

$\frac{{(4.9 \cdot 10^{3})}^{- 2} \cdot 7^{4} \cdot {(\frac{1}{700} \cdot \frac{1}{10^{10}})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{{(0.00007)}^{- 1}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(4.9 \cdot 10^{3})}^{- 2} \cdot 7^{4} \cdot {(\frac{1}{700} \cdot \frac{1}{10^{10}})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{\frac{1}{0.00007}}$

Step 1.2

Divide $1$ by $0.00007$ .

$\frac{{(4.9 \cdot 10^{3})}^{- 2} \cdot 7^{4} \cdot {(\frac{1}{700} \cdot \frac{1}{10^{10}})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 2

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

$\frac{{(4.9 \cdot 10^{3})}^{- 2} \cdot 7^{4} \cdot {(\frac{1}{700} \cdot \frac{1}{10000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the product rule to $4.9 \cdot 10^{3}$ .

$\frac{{4.9}^{- 2} \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{700} \cdot \frac{1}{10000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.2

Combine exponents.

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Step 3.2.1

Multiply $\frac{1}{700}$ by $\frac{1}{10000000000}$ .

$\frac{{4.9}^{- 2} \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{700 \cdot 10000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.2.2

Multiply $700$ by $10000000000$ .

$\frac{{4.9}^{- 2} \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{{4.9}^{2}} \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.4

Raise $4.9$ to the power of $2$ .

$\frac{\frac{1}{24.01} \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.5

Divide $1$ by $24.01$ .

$\frac{0.04164931 \cdot {(10^{3})}^{- 2} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.6

Multiply the exponents in ${(10^{3})}^{- 2}$ .

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Step 3.6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{0.04164931 \cdot 10^{3 \cdot - 2} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.6.2

Multiply $3$ by $- 2$ .

$\frac{0.04164931 \cdot 10^{- 6} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{0.04164931 \cdot \frac{1}{10^{6}} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.8

Raise $10$ to the power of $6$ .

$\frac{0.04164931 \cdot \frac{1}{1000000} \cdot 7^{4} {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.9

Raise $7$ to the power of $4$ .

$\frac{0.04164931 \cdot \frac{1}{1000000} \cdot 2401 {(\frac{1}{7000000000000})}^{- 1}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.10

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{0.04164931 \cdot \frac{1}{1000000} \cdot 2401 \cdot 7000000000000}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.11

Combine exponents.

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Step 3.11.1

Combine $0.04164931$ and $\frac{1}{1000000}$ .

$\frac{\frac{0.04164931}{1000000} \cdot 2401 \cdot 7000000000000}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.11.2

Combine $\frac{0.04164931}{1000000}$ and $2401$ .

$\frac{\frac{0.04164931 \cdot 2401}{1000000} \cdot 7000000000000}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.11.3

Multiply $0.04164931$ by $2401$ .

$\frac{\frac{100}{1000000} \cdot 7000000000000}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.11.4

Combine $\frac{100}{1000000}$ and $7000000000000$ .

$\frac{\frac{100 \cdot 7000000000000}{1000000}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.11.5

Multiply $100$ by $7000000000000$ .

$\frac{\frac{700000000000000}{1000000}}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 3.12

Divide $700000000000000$ by $1000000$ .

$\frac{700000000}{0.343 - 10^{- 2} \cdot 0.7 \cdot 10^{- 1}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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Step 4.1.1

Move $10^{- 1}$ .

$\frac{700000000}{0.343 - (10^{- 1} \cdot 10^{- 2}) \cdot 0.7} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.1.2

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

$\frac{700000000}{0.343 - 10^{- 1 - 2} \cdot 0.7} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.1.3

Subtract $2$ from $- 1$ .

$\frac{700000000}{0.343 - 10^{- 3} \cdot 0.7} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{700000000}{0.343 - \frac{1}{10^{3}} \cdot 0.7} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.3

Raise $10$ to the power of $3$ .

$\frac{700000000}{0.343 - \frac{1}{1000} \cdot 0.7} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.4

Multiply $- \frac{1}{1000} \cdot 0.7$ .

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Step 4.4.1

Multiply $0.7$ by $- 1$ .

$\frac{700000000}{0.343 - 0.7 (\frac{1}{1000})} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.4.2

Combine $- 0.7$ and $\frac{1}{1000}$ .

$\frac{700000000}{0.343 + \frac{- 0.7}{1000}} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.5

Divide $- 0.7$ by $1000$ .

$\frac{700000000}{0.343 - 0.0007} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 4.6

Subtract $0.0007$ from $0.343$ .

$\frac{700000000}{0.3423} \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 5

Simplify the expression.

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Step 5.1

Divide $700000000$ by $0.3423$ .

$2044989775.05112474 \cdot 2401 \cdot \frac{1}{14285.\overline{714285}}$

Step 5.2

Multiply $2044989775.05112474$ by $2401$ .

$4910020449897.75051124 \cdot \frac{1}{14285.\overline{714285}}$

Step 5.3

Divide $1$ by $14285.\overline{714285}$ .

$4910020449897.75051124 \cdot 0.00007$

Step 5.4

Multiply $4910020449897.75051124$ by $0.00007$ .

$343701431.49284253$