Basic Math Examples

$d^{4.62} = 1.39 a + 3$

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.

$d^{4 \frac{62}{100}} = 1.39 a + 3$

Step 1.2

Reduce the fractional part of the mixed number.

$d^{4 \frac{31}{50}} = 1.39 a + 3$

Step 1.3

Convert $4 \frac{31}{50}$ to an improper fraction.

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Step 1.3.1

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

$d^{4 + \frac{31}{50}} = 1.39 a + 3$

Step 1.3.2

Add $4$ and $\frac{31}{50}$ .

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Step 1.3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$d^{4 \cdot \frac{50}{50} + \frac{31}{50}} = 1.39 a + 3$

Step 1.3.2.2

Combine $4$ and $\frac{50}{50}$ .

$d^{\frac{4 \cdot 50}{50} + \frac{31}{50}} = 1.39 a + 3$

Step 1.3.2.3

Combine the numerators over the common denominator.

$d^{\frac{4 \cdot 50 + 31}{50}} = 1.39 a + 3$

Step 1.3.2.4

Simplify the numerator.

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Step 1.3.2.4.1

Multiply $4$ by $50$ .

$d^{\frac{200 + 31}{50}} = 1.39 a + 3$

Step 1.3.2.4.2

Add $200$ and $31$ .

$d^{\frac{231}{50}} = 1.39 a + 3$

Step 2

Raise each side of the equation to the power of $\frac{1}{4.62}$ to eliminate the fractional exponent on the left side.

${(d^{\frac{231}{50}})}^{\frac{1}{4.62}} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

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 ${(d^{\frac{231}{50}})}^{\frac{1}{4.62}}$ .

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Step 3.1.1.1

Multiply the exponents in ${(d^{\frac{231}{50}})}^{\frac{1}{4.62}}$ .

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Step 3.1.1.1.1

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

$d^{\frac{231}{50} \cdot \frac{1}{4.62}} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.1.1.1.2

Cancel the common factor of $4.62$ .

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Step 3.1.1.1.2.1

Factor $4.62$ out of $231$ .

$d^{\frac{4.62 (50)}{50} \cdot \frac{1}{4.62}} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.1.1.1.2.2

Cancel the common factor.

$d^{\frac{4.62 \cdot 50}{50} \cdot \frac{1}{4.62}} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.1.1.1.2.3

Rewrite the expression.

$d^{\frac{50}{50}} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.1.1.1.3

Divide $50$ by $50$ .

$d^{1} = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.1.1.2

Simplify.

$d = {(1.39 a + 3)}^{\frac{1}{4.62}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Divide $1$ by $4.62$ .

$d = {(1.39 a + 3)}^{0.\overline{216450}}$