Finite Math Examples

$75000 = x^{0.48 \cdot 13}$

Step 1

Rewrite the equation as $x^{0.48 \cdot 13} = 75000$ .

$x^{0.48 \cdot 13} = 75000$

Step 2

Multiply $0.48$ by $13$ .

$x^{6.24} = 75000$

Step 3

Convert the decimal exponent to a fractional exponent.

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Step 3.1

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.

$x^{6 \frac{24}{100}} = 75000$

Step 3.2

Reduce the fractional part of the mixed number.

$x^{6 \frac{6}{25}} = 75000$

Step 3.3

Convert $6 \frac{6}{25}$ to an improper fraction.

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Step 3.3.1

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

$x^{6 + \frac{6}{25}} = 75000$

Step 3.3.2

Add $6$ and $\frac{6}{25}$ .

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Step 3.3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$x^{6 \cdot \frac{25}{25} + \frac{6}{25}} = 75000$

Step 3.3.2.2

Combine $6$ and $\frac{25}{25}$ .

$x^{\frac{6 \cdot 25}{25} + \frac{6}{25}} = 75000$

Step 3.3.2.3

Combine the numerators over the common denominator.

$x^{\frac{6 \cdot 25 + 6}{25}} = 75000$

Step 3.3.2.4

Simplify the numerator.

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Step 3.3.2.4.1

Multiply $6$ by $25$ .

$x^{\frac{150 + 6}{25}} = 75000$

Step 3.3.2.4.2

Add $150$ and $6$ .

$x^{\frac{156}{25}} = 75000$

Step 4

Raise each side of the equation to the power of $\frac{1}{6.24}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{156}{25}})}^{\frac{1}{6.24}} = 75000^{\frac{1}{6.24}}$

Step 5

Simplify the exponent.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify ${(x^{\frac{156}{25}})}^{\frac{1}{6.24}}$ .

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Step 5.1.1.1

Multiply the exponents in ${(x^{\frac{156}{25}})}^{\frac{1}{6.24}}$ .

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Step 5.1.1.1.1

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

$x^{\frac{156}{25} \cdot \frac{1}{6.24}} = 75000^{\frac{1}{6.24}}$

Step 5.1.1.1.2

Cancel the common factor of $6.24$ .

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Step 5.1.1.1.2.1

Factor $6.24$ out of $156$ .

$x^{\frac{6.24 (25)}{25} \cdot \frac{1}{6.24}} = 75000^{\frac{1}{6.24}}$

Step 5.1.1.1.2.2

Cancel the common factor.

$x^{\frac{6.24 \cdot 25}{25} \cdot \frac{1}{6.24}} = 75000^{\frac{1}{6.24}}$

Step 5.1.1.1.2.3

Rewrite the expression.

$x^{\frac{25}{25}} = 75000^{\frac{1}{6.24}}$

Step 5.1.1.1.3

Divide $25$ by $25$ .

$x^{1} = 75000^{\frac{1}{6.24}}$

Step 5.1.1.2

Simplify.

$x = 75000^{\frac{1}{6.24}}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $75000^{\frac{1}{6.24}}$ .

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Step 5.2.1.1

Divide $1$ by $6.24$ .

$x = 75000^{0.16025641}$

Step 5.2.1.2

Raise $75000$ to the power of $0.16025641$ .

$x = 6.04310051$