Problem 58 - College Algebra Essentials

Question

Simplify each exponential expression. $$\frac{10 x^{4} y^{9}}{30 x^{12} y^{-3}}$$

Step-by-Step Solution

Answer

\((1/3) * x^{-8} * y^{12}\) is the simplified form of the given exponential expression.

Step 1: Simplify Coefficients

When we simplify the coefficients \(10/30\), we get \(1/3\). So the fraction becomes \(1/3\cdot \frac{x^{4} y^{9}}{x^{12} y^{-3}}\).

Step 2: Simplify x terms

To simplify the x terms, we subtract the exponent of the denominator from the exponent of the numerator. Hence, \(x^{4}/x^{12} = x^{4-12} = x^{-8}\).

Step 3: Simplify y terms

Similarly, we simplify the y terms. Hence, \(y^{9}/y^{-3} = y^{9-(-3)} = y^{12}\).

Step 4: Combine all terms

Combine all the simplified terms together. Hence, we get \((1/3) * x^{-8} * y^{12}\).