Basic Math Examples

$2550 {(1 + a)}^{11} = 3905$

Step 1

Divide each term in $2550 {(1 + a)}^{11} = 3905$ by $2550$ and simplify.

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Step 1.1

Divide each term in $2550 {(1 + a)}^{11} = 3905$ by $2550$ .

$\frac{2550 {(1 + a)}^{11}}{2550} = \frac{3905}{2550}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2550$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2550 {(1 + a)}^{11}}{2550} = \frac{3905}{2550}$

Step 1.2.1.2

Divide ${(1 + a)}^{11}$ by $1$ .

${(1 + a)}^{11} = \frac{3905}{2550}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $3905$ and $2550$ .

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Step 1.3.1.1

Factor $5$ out of $3905$ .

${(1 + a)}^{11} = \frac{5 (781)}{2550}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $5$ out of $2550$ .

${(1 + a)}^{11} = \frac{5 \cdot 781}{5 \cdot 510}$

Step 1.3.1.2.2

Cancel the common factor.

${(1 + a)}^{11} = \frac{5 \cdot 781}{5 \cdot 510}$

Step 1.3.1.2.3

Rewrite the expression.

${(1 + a)}^{11} = \frac{781}{510}$

Step 2

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

$1 + a = \sqrt[11]{\frac{781}{510}}$

Step 3

Rewrite $\sqrt[11]{\frac{781}{510}}$ as $\frac{\sqrt[11]{781}}{\sqrt[11]{510}}$ .

$1 + a = \frac{\sqrt[11]{781}}{\sqrt[11]{510}}$

Step 4

Subtract $1$ from both sides of the equation.

$a = \frac{\sqrt[11]{781}}{\sqrt[11]{510}} - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{\sqrt[11]{781}}{\sqrt[11]{510}} - 1$

Decimal Form:

$a = 0.03950248 \dots$