Finite Math Examples

$11 b^{\frac{4}{3}} = 77$

Step 1

Divide each term in $11 b^{\frac{4}{3}} = 77$ by $11$ and simplify.

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Step 1.1

Divide each term in $11 b^{\frac{4}{3}} = 77$ by $11$ .

$\frac{11 b^{\frac{4}{3}}}{11} = \frac{77}{11}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor.

$\frac{11 b^{\frac{4}{3}}}{11} = \frac{77}{11}$

Step 1.2.2

Divide $b^{\frac{4}{3}}$ by $1$ .

$b^{\frac{4}{3}} = \frac{77}{11}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $77$ by $11$ .

$b^{\frac{4}{3}} = 7$

Step 2

Raise each side of the equation to the power of $\frac{3}{4}$ to eliminate the fractional exponent on the left side.

${(b^{\frac{4}{3}})}^{\frac{3}{4}} = \pm 7^{\frac{3}{4}}$

Step 3

Simplify the left side.

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Step 3.1

Simplify ${(b^{\frac{4}{3}})}^{\frac{3}{4}}$ .

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Step 3.1.1

Multiply the exponents in ${(b^{\frac{4}{3}})}^{\frac{3}{4}}$ .

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Step 3.1.1.1

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

$b^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 7^{\frac{3}{4}}$

Step 3.1.1.2

Cancel the common factor of $4$ .

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Step 3.1.1.2.1

Cancel the common factor.

$b^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 7^{\frac{3}{4}}$

Step 3.1.1.2.2

Rewrite the expression.

$b^{\frac{1}{3} \cdot 3} = \pm 7^{\frac{3}{4}}$

Step 3.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.3.1

Cancel the common factor.

$b^{\frac{1}{3} \cdot 3} = \pm 7^{\frac{3}{4}}$

Step 3.1.1.3.2

Rewrite the expression.

$b^{1} = \pm 7^{\frac{3}{4}}$

Step 3.1.2

Simplify.

$b = \pm 7^{\frac{3}{4}}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$b = 7^{\frac{3}{4}}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$b = - 7^{\frac{3}{4}}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$b = 7^{\frac{3}{4}}, - 7^{\frac{3}{4}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = 7^{\frac{3}{4}}, - 7^{\frac{3}{4}}$

Decimal Form:

$b = 4.30351707 \dots, - 4.30351707 \dots$