Pre-Algebra Examples

$5 = 9.6 {(b)}^{13.5}$

Step 1

Rewrite the equation as $9.6 b^{13.5} = 5$ .

$9.6 b^{13.5} = 5$

Step 2

Divide each term in $9.6 b^{13.5} = 5$ by $9.6$ and simplify.

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Step 2.1

Divide each term in $9.6 b^{13.5} = 5$ by $9.6$ .

$\frac{9.6 b^{13.5}}{9.6} = \frac{5}{9.6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9.6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9.6 b^{13.5}}{9.6} = \frac{5}{9.6}$

Step 2.2.1.2

Divide $b^{13.5}$ by $1$ .

$b^{13.5} = \frac{5}{9.6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $5$ by $9.6$ .

$b^{13.5} = 0.5208\overline{3}$

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 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.

$b^{13 \frac{5}{10}} = 0.5208\overline{3}$

Step 3.2

Reduce the fractional part of the mixed number.

$b^{13 \frac{1}{2}} = 0.5208\overline{3}$

Step 3.3

Convert $13 \frac{1}{2}$ to an improper fraction.

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Step 3.3.1

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

$b^{13 + \frac{1}{2}} = 0.5208\overline{3}$

Step 3.3.2

Add $13$ and $\frac{1}{2}$ .

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Step 3.3.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b^{13 \cdot \frac{2}{2} + \frac{1}{2}} = 0.5208\overline{3}$

Step 3.3.2.2

Combine $13$ and $\frac{2}{2}$ .

$b^{\frac{13 \cdot 2}{2} + \frac{1}{2}} = 0.5208\overline{3}$

Step 3.3.2.3

Combine the numerators over the common denominator.

$b^{\frac{13 \cdot 2 + 1}{2}} = 0.5208\overline{3}$

Step 3.3.2.4

Simplify the numerator.

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Step 3.3.2.4.1

Multiply $13$ by $2$ .

$b^{\frac{26 + 1}{2}} = 0.5208\overline{3}$

Step 3.3.2.4.2

Add $26$ and $1$ .

$b^{\frac{27}{2}} = 0.5208\overline{3}$

Step 4

Raise each side of the equation to the power of $\frac{1}{13.5}$ to eliminate the fractional exponent on the left side.

${(b^{\frac{27}{2}})}^{\frac{1}{13.5}} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

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 ${(b^{\frac{27}{2}})}^{\frac{1}{13.5}}$ .

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Step 5.1.1.1

Multiply the exponents in ${(b^{\frac{27}{2}})}^{\frac{1}{13.5}}$ .

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Step 5.1.1.1.1

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

$b^{\frac{27}{2} \cdot \frac{1}{13.5}} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.1.1.1.2

Cancel the common factor of $13.5$ .

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Step 5.1.1.1.2.1

Factor $13.5$ out of $27$ .

$b^{\frac{13.5 (2)}{2} \cdot \frac{1}{13.5}} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.1.1.1.2.2

Cancel the common factor.

$b^{\frac{13.5 \cdot 2}{2} \cdot \frac{1}{13.5}} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.1.1.1.2.3

Rewrite the expression.

$b^{\frac{2}{2}} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.1.1.1.3

Divide $2$ by $2$ .

$b^{1} = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.1.1.2

Simplify.

$b = {0.5208\overline{3}}^{\frac{1}{13.5}}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify ${0.5208\overline{3}}^{\frac{1}{13.5}}$ .

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Step 5.2.1.1

Divide $1$ by $13.5$ .

$b = {0.5208\overline{3}}^{0.\overline{074}}$

Step 5.2.1.2

Raise $0.5208\overline{3}$ to the power of $0.\overline{074}$ .

$b = 0.95282846$