Problem 50 - College Algebra Essentials

Question

Simplify each exponential expression. $$\frac{20 x^{24}}{10 x^{6}}$$

Step-by-Step Solution

Answer

The simplification of the given exponential expression is \(2x^{18}\).

Step 1: Fraction Simplification

First, simplify the fraction part of the expression, which is \(\frac{20}{10}\). This simplifies to 2.

Step 2: Apply Exponent Law

The law of exponents states that to divide the same bases, you subtract the exponents. So the exponential part of the expression, \( x^{24} ÷ x^{6}\), becomes \(x^{24-6}\).

Step 3: Subtract the Exponents

Subtract the exponents to get \(x^{18}\).

Step 4: Combine The Results

Combine the results from step 1 and step 3. Multiply the simplified fraction (2) with the result from the exponent ( \(x^{18}\) ). So, the expression can be simplified to \(2x^{18}\).