Basic Math Examples

$2800 = 2300 {(1 + r)}^{5}$

Step 1

Rewrite the equation as $2300 {(1 + r)}^{5} = 2800$ .

$2300 {(1 + r)}^{5} = 2800$

Step 2

Divide each term in $2300 {(1 + r)}^{5} = 2800$ by $2300$ and simplify.

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Step 2.1

Divide each term in $2300 {(1 + r)}^{5} = 2800$ by $2300$ .

$\frac{2300 {(1 + r)}^{5}}{2300} = \frac{2800}{2300}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2300$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2300 {(1 + r)}^{5}}{2300} = \frac{2800}{2300}$

Step 2.2.1.2

Divide ${(1 + r)}^{5}$ by $1$ .

${(1 + r)}^{5} = \frac{2800}{2300}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2800$ and $2300$ .

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Step 2.3.1.1

Factor $100$ out of $2800$ .

${(1 + r)}^{5} = \frac{100 (28)}{2300}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $100$ out of $2300$ .

${(1 + r)}^{5} = \frac{100 \cdot 28}{100 \cdot 23}$

Step 2.3.1.2.2

Cancel the common factor.

${(1 + r)}^{5} = \frac{100 \cdot 28}{100 \cdot 23}$

Step 2.3.1.2.3

Rewrite the expression.

${(1 + r)}^{5} = \frac{28}{23}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$1 + r = \sqrt[5]{\frac{28}{23}}$

Step 4

Simplify $\sqrt[5]{\frac{28}{23}}$ .

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Step 4.1

Rewrite $\sqrt[5]{\frac{28}{23}}$ as $\frac{\sqrt[5]{28}}{\sqrt[5]{23}}$ .

$1 + r = \frac{\sqrt[5]{28}}{\sqrt[5]{23}}$

Step 4.2

Multiply $\frac{\sqrt[5]{28}}{\sqrt[5]{23}}$ by $\frac{{\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{4}}$ .

$1 + r = \frac{\sqrt[5]{28}}{\sqrt[5]{23}} \cdot \frac{{\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{4}}$

Step 4.3

Combine and simplify the denominator.

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Step 4.3.1

Multiply $\frac{\sqrt[5]{28}}{\sqrt[5]{23}}$ by $\frac{{\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{4}}$ .

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{\sqrt[5]{23} {\sqrt[5]{23}}^{4}}$

Step 4.3.2

Raise $\sqrt[5]{23}$ to the power of $1$ .

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{1} {\sqrt[5]{23}}^{4}}$

Step 4.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{1 + 4}}$

Step 4.3.4

Add $1$ and $4$ .

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{{\sqrt[5]{23}}^{5}}$

Step 4.3.5

Rewrite ${\sqrt[5]{23}}^{5}$ as $23$ .

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Step 4.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{23}$ as $23^{\frac{1}{5}}$ .

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{{(23^{\frac{1}{5}})}^{5}}$

Step 4.3.5.2

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

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{23^{\frac{1}{5} \cdot 5}}$

Step 4.3.5.3

Combine $\frac{1}{5}$ and $5$ .

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{23^{\frac{5}{5}}}$

Step 4.3.5.4

Cancel the common factor of $5$ .

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Step 4.3.5.4.1

Cancel the common factor.

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{23^{\frac{5}{5}}}$

Step 4.3.5.4.2

Rewrite the expression.

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{23^{1}}$

Step 4.3.5.5

Evaluate the exponent.

$1 + r = \frac{\sqrt[5]{28} {\sqrt[5]{23}}^{4}}{23}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Rewrite ${\sqrt[5]{23}}^{4}$ as $\sqrt[5]{23^{4}}$ .

$1 + r = \frac{\sqrt[5]{28} \sqrt[5]{23^{4}}}{23}$

Step 4.4.2

Raise $23$ to the power of $4$ .

$1 + r = \frac{\sqrt[5]{28} \sqrt[5]{279841}}{23}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Combine using the product rule for radicals.

$1 + r = \frac{\sqrt[5]{28 \cdot 279841}}{23}$

Step 4.5.2

Multiply $28$ by $279841$ .

$1 + r = \frac{\sqrt[5]{7835548}}{23}$

Step 5

Subtract $1$ from both sides of the equation.

$r = \frac{\sqrt[5]{7835548}}{23} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\sqrt[5]{7835548}}{23} - 1$

Decimal Form:

$r = 0.04012620 \dots$