Basic Math Examples

$\frac{1}{2} \cdot (o f^{2.6}) = 1.3$

Step 1

Multiply both sides of the equation by

$2$ .

$2 (\frac{1}{2} \cdot (o f^{2.6})) = 2 \cdot 1.3$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

$2 (\frac{1}{2} \cdot (o f^{2.6}))$ .

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Step 2.1.1.1

Multiply

$\frac{1}{2} (o f^{2.6})$ .

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Step 2.1.1.1.1

Combine

$o$ and

$\frac{1}{2}$ .

$2 (\frac{o}{2} f^{2.6}) = 2 \cdot 1.3$

Step 2.1.1.1.2

Combine

$\frac{o}{2}$ and

$f^{2.6}$ .

$2 \frac{o f^{2.6}}{2} = 2 \cdot 1.3$

Step 2.1.1.2

Cancel the common factor of

$2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{o f^{2.6}}{2} = 2 \cdot 1.3$

Step 2.1.1.2.2

Rewrite the expression.

$o f^{2.6} = 2 \cdot 1.3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

$2$ by

$1.3$ .

$o f^{2.6} = 2.6$

Step 3

Divide each term in

$o f^{2.6} = 2.6$ by

$o$ and simplify.

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Step 3.1

Divide each term in

$o f^{2.6} = 2.6$ by

$o$ .

$\frac{o f^{2.6}}{o} = \frac{2.6}{o}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$o$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{o f^{2.6}}{o} = \frac{2.6}{o}$

Step 3.2.1.2

Divide

$f^{2.6}$ by

$1$ .

$f^{2.6} = \frac{2.6}{o}$

Step 4

Convert the decimal exponent to a fractional exponent.

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Step 4.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is

$1$ number to the right of the decimal point, place the decimal number over

$10^{1}$

$(10)$ . Next, add the whole number to the left of the decimal.

$f^{2 \frac{6}{10}} = \frac{2.6}{o}$

Step 4.2

Reduce the fractional part of the mixed number.

$f^{2 \frac{3}{5}} = \frac{2.6}{o}$

Step 4.3

Convert

$2 \frac{3}{5}$ to an improper fraction.

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Step 4.3.1

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

$f^{2 + \frac{3}{5}} = \frac{2.6}{o}$

Step 4.3.2

Add

$2$ and

$\frac{3}{5}$ .

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Step 4.3.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$f^{2 \cdot \frac{5}{5} + \frac{3}{5}} = \frac{2.6}{o}$

Step 4.3.2.2

Combine

$2$ and

$\frac{5}{5}$ .

$f^{\frac{2 \cdot 5}{5} + \frac{3}{5}} = \frac{2.6}{o}$

Step 4.3.2.3

Combine the numerators over the common denominator.

$f^{\frac{2 \cdot 5 + 3}{5}} = \frac{2.6}{o}$

Step 4.3.2.4

Simplify the numerator.

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Step 4.3.2.4.1

Multiply

$2$ by

$5$ .

$f^{\frac{10 + 3}{5}} = \frac{2.6}{o}$

Step 4.3.2.4.2

Add

$10$ and

$3$ .

$f^{\frac{13}{5}} = \frac{2.6}{o}$

Step 5

Raise each side of the equation to the power of

$\frac{1}{2.6}$ to eliminate the fractional exponent on the left side.

${(f^{\frac{13}{5}})}^{\frac{1}{2.6}} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6

Simplify the exponent.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify

${(f^{\frac{13}{5}})}^{\frac{1}{2.6}}$ .

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Step 6.1.1.1

Multiply the exponents in

${(f^{\frac{13}{5}})}^{\frac{1}{2.6}}$ .

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Step 6.1.1.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$f^{\frac{13}{5} \cdot \frac{1}{2.6}} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.1.1.1.2

Cancel the common factor of

$2.6$ .

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Step 6.1.1.1.2.1

Factor

$2.6$ out of

$13$ .

$f^{\frac{2.6 (5)}{5} \cdot \frac{1}{2.6}} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.1.1.1.2.2

Cancel the common factor.

$f^{\frac{2.6 \cdot 5}{5} \cdot \frac{1}{2.6}} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.1.1.1.2.3

Rewrite the expression.

$f^{\frac{5}{5}} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.1.1.1.3

Divide

$5$ by

$5$ .

$f^{1} = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.1.1.2

Simplify.

$f = {(\frac{2.6}{o})}^{\frac{1}{2.6}}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify

${(\frac{2.6}{o})}^{\frac{1}{2.6}}$ .

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Step 6.2.1.1

Divide

$1$ by

$2.6$ .

$f = {(\frac{2.6}{o})}^{0.\overline{384615}}$

Step 6.2.1.2

Apply the product rule to

$\frac{2.6}{o}$ .

$f = \frac{{2.6}^{0.\overline{384615}}}{o^{0.\overline{384615}}}$

Step 6.2.1.3

Raise

$2.6$ to the power of

$0.\overline{384615}$ .

$f = \frac{1.44412615}{o^{0.\overline{384615}}}$