# How do you simplify x^2y^-4*x^3y^2 and write it using only positive exponents?

Jan 29, 2017

x^5/y^2 larr" Matching the "ul("format requested in the question")

${x}^{5} {y}^{- 2} \leftarrow \text{ Matching format in the question}$

#### Explanation:

Write as ${x}^{2} / {y}^{4} \times {x}^{3} {y}^{2}$

This is the same as:

${x}^{2} \times {x}^{3} \times {y}^{2} / {y}^{4}$

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

${x}^{5} / {y}^{2}$

However, it is good practice to use the same format as in the question.

Write as: ${x}^{5} {y}^{- 2}$

Mar 28, 2018

${x}^{5} / {y}^{2}$

#### Explanation:

x^2 y^−4⋅x^3 y^2

This is just a long multiplication problem. All the variables are factors, even though there is one multiplication dot written between two of the factors.

That means you can just write this out as four factors, like this:

x^2 * y^(−4)⋅x^3 * y^2

You can re-group the factors for your own convenience

$\left({x}^{2}\right) \left({x}^{3}\right) \times \left({y}^{- 4}\right) \left({y}^{2}\right)$

To multiply like bases, you add their exponents
${x}^{2 + 3} \times {y}^{- 4 + 2}$

This comes out to
x^5  y^-2 $\leftarrow$ answer

To clear the minus sign on the exponent of $y$, flip it into the denominator and reverse the sign

${x}^{5} / {y}^{2}$ $\leftarrow$ same answer