Basic Math Examples

$\frac{{(1.16 \cdot 10^{- 23})}^{2}}{(4.98 \cdot 10^{- 24}) \cdot (9.9 \cdot 10^{- 24})}$

Step 1

Multiply $4.98$ by $9.9$ .

$\frac{{(1.16 \cdot 10^{- 23})}^{2}}{49.302 (10^{- 24} \cdot 10^{- 24})}$

Step 2

Multiply $10^{- 24}$ by $10^{- 24}$ by adding the exponents.

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Step 2.1

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

$\frac{{(1.16 \cdot 10^{- 23})}^{2}}{49.302 \cdot 10^{- 24 - 24}}$

Step 2.2

Subtract $24$ from $- 24$ .

$\frac{{(1.16 \cdot 10^{- 23})}^{2}}{49.302 \cdot 10^{- 48}}$

Step 3

Move $10^{- 48}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(1.16 \cdot 10^{- 23})}^{2} \cdot 10^{48}}{49.302}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the product rule to $1.16 \cdot 10^{- 23}$ .

$\frac{{1.16}^{2} \cdot {(10^{- 23})}^{2} \cdot 10^{48}}{49.302}$

Step 4.2

Raise $1.16$ to the power of $2$ .

$\frac{1.3456 \cdot {(10^{- 23})}^{2} \cdot 10^{48}}{49.302}$

Step 4.3

Multiply the exponents in ${(10^{- 23})}^{2}$ .

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Step 4.3.1

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

$\frac{1.3456 \cdot 10^{- 23 \cdot 2} \cdot 10^{48}}{49.302}$

Step 4.3.2

Multiply $- 23$ by $2$ .

$\frac{1.3456 \cdot 10^{- 46} \cdot 10^{48}}{49.302}$

Step 4.4

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

$\frac{1.3456 \cdot \frac{1}{10^{46}} \cdot 10^{48}}{49.302}$

Step 4.5

Combine exponents.

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Step 4.5.1

Combine $1.3456$ and $\frac{1}{10^{46}}$ .

$\frac{\frac{1.3456}{10^{46}} \cdot 10^{48}}{49.302}$

Step 4.5.2

Combine $\frac{1.3456}{10^{46}}$ and $10^{48}$ .

$\frac{\frac{1.3456 \cdot 10^{48}}{10^{46}}}{49.302}$

Step 4.6

Reduce the expression by cancelling the common factors.

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Step 4.6.1

Reduce the expression $\frac{1.3456 \cdot 10^{48}}{10^{46}}$ by cancelling the common factors.

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Step 4.6.1.1

Factor $10^{46}$ out of $1.3456 \cdot 10^{48}$ .

$\frac{\frac{10^{46} \cdot 1.3456 \cdot 10^{2}}{10^{46}}}{49.302}$

Step 4.6.1.2

Multiply by $1$ .

$\frac{\frac{10^{46} \cdot 1.3456 \cdot 10^{2}}{10^{46} \cdot 1}}{49.302}$

Step 4.6.1.3

Cancel the common factor.

$\frac{\frac{10^{46} \cdot 1.3456 \cdot 10^{2}}{10^{46} \cdot 1}}{49.302}$

Step 4.6.1.4

Rewrite the expression.

$\frac{\frac{1.3456 \cdot 10^{2}}{1}}{49.302}$

Step 4.6.2

Divide $1.3456 \cdot 10^{2}$ by $1$ .

$\frac{1.3456 \cdot 10^{2}}{49.302}$

Step 4.7

Raise $10$ to the power of $2$ .

$\frac{1.3456 \cdot 100}{49.302}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $1.3456$ by $100$ .

$\frac{134.56}{49.302}$

Step 5.2

Divide $134.56$ by $49.302$ .

$2.72930104$