Precalculus Examples

$(\frac{1^{2}}{11}) = \frac{1}{121}$

Step 1

Simplify.

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Step 1.1

Divide each term in $(\frac{1^{2}}{11}) = \frac{1}{121}$ by $(\frac{1^{2}}{11})$ .

$\frac{(\frac{1^{2}}{11})}{(\frac{1^{2}}{11})} = \frac{\frac{1}{121}}{(\frac{1^{2}}{11})}$

Step 1.2

One to any power is one.

$\frac{\frac{1}{121}}{\frac{1}{11}}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{121} \cdot 11$

Step 1.4

Cancel the common factor of $11$ .

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Step 1.4.1

Factor $11$ out of $121$ .

$\frac{1}{11 (11)} \cdot 11$

Step 1.4.2

Cancel the common factor.

$\frac{1}{11 \cdot 11} \cdot 11$

Step 1.4.3

Rewrite the expression.

$\frac{1}{11}$

Step 1.5

Reduce by cancelling the common factors.

$1^{2} = \frac{1}{11}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1)$ of the right side $(\frac{1}{11})$ equals the exponent $(2)$ .

$\log_{1} (\frac{1}{11}) = 2$