Problem 52 - College Algebra Essentials

Question

Simplify each exponential expression. $$\frac{35 a^{14} b^{6}}{-7 a^{7} b^{3}}$$

Step-by-Step Solution

Answer

The simplified form for the expression is: \( -5 a^{7} b^{3} \)

Step 1: Simplify the Constants

The first step involves simplifying the constants. Divide 35 by -7 to get -5. So the expression becomes \( -5 \frac{a^{14} b^{6}}{a^{7} b^{3}} \)

Step 2: Apply Exponent Rules to 'a'

In the next step, apply the quotient rule to the base 'a'. Subtract the exponent in the denominator from the exponent in the numerator, \(14 - 7 = 7\). This gives us \( -5 a^{7} \frac{b^{6}}{b^{3}} \)

Step 3: Apply Exponent Rules to 'b'

Follow the same process for the base 'b'. The operation gives us \(3\) as the new exponent. We can confirm this by subtracting \(3\) from \(6\). The final simplified expression thus is: \( -5 a^{7} b^{3} \)