Question

Simplify without a negative exponent.



18x2y−218x^2y^{-2}18x
2
y
−2

Answer 1

To simplify the expression \( 18x^2y - 218x^2y^{-2} \), we first rewrite the term with the negative exponent:

\[
18x^2y^{-2} = \frac{18x^2}{y^2}
\]

Now let's rewrite the original expression:

\[
18x^2y - 218x^2y^{-2} = 18x^2y - 218 \cdot \frac{x^2}{y^2}
\]

Next, we will combine these two terms over a common denominator. The common denominator here is \( y^2 \):

1. Rewrite \( 18x^2y \) so it has the common denominator \( y^2 \):
\[
18x^2y = 18x^2 \cdot \frac{y^3}{y^2} = \frac{18x^2y^3}{y^2}
\]

2. Now we can write the expression with a common denominator:
\[
\frac{18x^2y^3}{y^2} - \frac{218x^2}{y^2}
\]

3. Combine the fractions:
\[
\frac{18x^2y^3 - 218x^2}{y^2}
\]

Now, factor out \( 2x^2 \) from the numerator:

\[
18x^2y^3 - 218x^2 = 2x^2 (9y^3 - 109)
\]

Thus, our expression simplifies to:

\[
\frac{2x^2 (9y^3 - 109)}{y^2}
\]

This is the simplified form of the expression without any negative exponents.