Precalculus Examples

${(2.718281 x)}^{0.28} = 9923.47$

Step 1

Convert the decimal exponent to a fractional exponent.

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Step 1.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are $2$ numbers to the right of the decimal point, place the decimal number over $10^{2}$ $(100)$ . Next, add the whole number to the left of the decimal.

${(2.718281 x)}^{0 \frac{28}{100}} = 9923.47$

Step 1.2

Reduce the fraction.

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Step 1.2.1

Convert $0 \frac{28}{100}$ to an improper fraction.

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Step 1.2.1.1

A mixed number is an addition of its whole and fractional parts.

${(2.718281 x)}^{0 + \frac{28}{100}} = 9923.47$

Step 1.2.1.2

Add $0$ and $\frac{28}{100}$ .

${(2.718281 x)}^{\frac{28}{100}} = 9923.47$

Step 1.2.2

Cancel the common factor of $28$ and $100$ .

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Step 1.2.2.1

Factor $4$ out of $28$ .

${(2.718281 x)}^{\frac{4 (7)}{100}} = 9923.47$

Step 1.2.2.2

Cancel the common factors.

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Step 1.2.2.2.1

Factor $4$ out of $100$ .

${(2.718281 x)}^{\frac{4 \cdot 7}{4 \cdot 25}} = 9923.47$

Step 1.2.2.2.2

Cancel the common factor.

${(2.718281 x)}^{\frac{4 \cdot 7}{4 \cdot 25}} = 9923.47$

Step 1.2.2.2.3

Rewrite the expression.

${(2.718281 x)}^{\frac{7}{25}} = 9923.47$

Step 2

Raise each side of the equation to the power of $\frac{1}{0.28}$ to eliminate the fractional exponent on the left side.

${({(2.718281 x)}^{\frac{7}{25}})}^{\frac{1}{0.28}} = {9923.47}^{\frac{1}{0.28}}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${({(2.718281 x)}^{\frac{7}{25}})}^{\frac{1}{0.28}}$ .

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Step 3.1.1.1

Multiply the exponents in ${({(2.718281 x)}^{\frac{7}{25}})}^{\frac{1}{0.28}}$ .

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Step 3.1.1.1.1

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

${(2.718281 x)}^{\frac{7}{25} \cdot \frac{1}{0.28}} = {9923.47}^{\frac{1}{0.28}}$

Step 3.1.1.1.2

Cancel the common factor of $0.28$ .

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Step 3.1.1.1.2.1

Factor $0.28$ out of $7$ .

${(2.718281 x)}^{\frac{0.28 (25)}{25} \cdot \frac{1}{0.28}} = {9923.47}^{\frac{1}{0.28}}$

Step 3.1.1.1.2.2

Cancel the common factor.

${(2.718281 x)}^{\frac{0.28 \cdot 25}{25} \cdot \frac{1}{0.28}} = {9923.47}^{\frac{1}{0.28}}$

Step 3.1.1.1.2.3

Rewrite the expression.

${(2.718281 x)}^{\frac{25}{25}} = {9923.47}^{\frac{1}{0.28}}$

Step 3.1.1.1.3

Divide $25$ by $25$ .

${(2.718281 x)}^{1} = {9923.47}^{\frac{1}{0.28}}$

Step 3.1.1.2

Simplify.

$2.718281 x = {9923.47}^{\frac{1}{0.28}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify ${9923.47}^{\frac{1}{0.28}}$ .

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Step 3.2.1.1

Divide $1$ by $0.28$ .

$2.718281 x = {9923.47}^{3.\overline{571428}}$

Step 3.2.1.2

Raise $9923.47$ to the power of $3.\overline{571428}$ .

$2.718281 x = 187844477878356$

Step 4

Divide each term in $2.718281 x = 187844477878356$ by $2.718281$ and simplify.

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Step 4.1

Divide each term in $2.718281 x = 187844477878356$ by $2.718281$ .

$\frac{2.718281 x}{2.718281} = \frac{187844477878356}{2.718281}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2.718281$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2.718281 x}{2.718281} = \frac{187844477878356}{2.718281}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{187844477878356}{2.718281}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $187844477878356$ by $2.718281$ .

$x = 69104142610111.31667403$