# How do you simplify (2x^2y^3)/(8xy^7)?

Feb 6, 2017

The simplified expression is $\frac{x}{4 {y}^{4}}$.

#### Explanation:

To simplify a mathematical expression or equation, we must combine the like terms by performing the required mathematical operation. In our expression, the like terms are: $2$ and $8$, ${x}^{2}$ and $x$, ${y}^{3}$ and ${y}^{7}$.

First, let us divide $2$ by $8$. The quotient is $\frac{1}{4}$.
$\frac{\left(2\right) {x}^{2} {y}^{3}}{\left(8\right) x {y}^{7}}$

Now the expression becomes like this. It is not needed to write the $1$ down.
$\frac{{x}^{2} {y}^{3}}{4 x {y}^{7}}$

Next, divide ${x}^{2}$ by $x$. Law of exponents state that "when dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent." In this case, this simply means:
$\frac{\left({x}^{2}\right) {y}^{3}}{4 \left(x\right) {y}^{7}} \implies {x}^{2 - 1} \implies x \mathmr{and} \frac{x}{1}$

Put the $x$ in the numerator. The expression is now like this. Now we are down to our final step.
$\frac{x {y}^{3}}{4 {y}^{7}}$

Repeat the previous step, only instead, we are now dividing ${y}^{3}$ by ${y}^{7}$.
$\frac{x \left({y}^{3}\right)}{4 \left({y}^{7}\right)} \implies {y}^{3 - 7} \implies {y}^{-} 4$
Law of exponents state again that "when a base is raised to a negative power, find the reciprocal of the base, keep the exponent with the original base, and drop the negative." (To find the reciprocal of a fraction, just switch the numerator and denominator!) This means:
${y}^{-} 4 \mathmr{and} \frac{1}{y} ^ 4$

Now this is our simplified expression. Hope this helps.
$\frac{x}{4 {y}^{4}}$

http://people.sunyulster.edu/nicholsm/webct/WebCT2/laws_of_exponents.htm