Finite Math Examples

$\frac{1}{x^{- 2} + y^{- 5}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\frac{1}{x^{2}} + y^{- 5}}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\frac{1}{x^{2}} + \frac{1}{y^{5}}}$

Step 1.3

To write $\frac{1}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{y^{5}}{y^{5}}$ .

$\frac{1}{\frac{1}{x^{2}} \cdot \frac{y^{5}}{y^{5}} + \frac{1}{y^{5}}}$

Step 1.4

To write $\frac{1}{y^{5}}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{1}{\frac{1}{x^{2}} \cdot \frac{y^{5}}{y^{5}} + \frac{1}{y^{5}} \cdot \frac{x^{2}}{x^{2}}}$

Step 1.5

Write each expression with a common denominator of $x^{2} y^{5}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.5.1

Multiply $\frac{1}{x^{2}}$ by $\frac{y^{5}}{y^{5}}$ .

$\frac{1}{\frac{y^{5}}{x^{2} y^{5}} + \frac{1}{y^{5}} \cdot \frac{x^{2}}{x^{2}}}$

Step 1.5.2

Multiply $\frac{1}{y^{5}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{1}{\frac{y^{5}}{x^{2} y^{5}} + \frac{x^{2}}{y^{5} x^{2}}}$

Step 1.5.3

Reorder the factors of $x^{2} y^{5}$ .

$\frac{1}{\frac{y^{5}}{y^{5} x^{2}} + \frac{x^{2}}{y^{5} x^{2}}}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{1}{\frac{y^{5} + x^{2}}{y^{5} x^{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{y^{5} x^{2}}{y^{5} + x^{2}}$

Step 3

Multiply $\frac{y^{5} x^{2}}{y^{5} + x^{2}}$ by $1$ .

$\frac{y^{5} x^{2}}{y^{5} + x^{2}}$