Chapter 4, Problem 6CST

To determine

To determine which expression is equivalent to $\frac{15b^9}{25b^3}$

Answer to Problem 6CST

F. $\frac{3b^3}{5}$

Explanation of Solution

Given information:

Expression $\frac{15b^9}{25b^3}$

Formula Used: Quotient Exponent Rule with Same base

Calculation:

To identify the equivalent expression, evaluate the given expression.

15 & 25 will be broken down into its prime factors.

The Product Rule with same base says that when the bases are same and in division, the exponent powers are subtracted. In the given expression, the base as b. On applying the Product Rule, get-

  $\frac{15b^9}{25b^3}=\frac{3\times 5\times b^{9-3}}{5\times 5}$

Since 5 is common in both numerator & denominator, it will cancel out. This will further give us-

  $=\frac{3b^3}{5}$

Hence F is correct.

Conclusion-

F. $\frac{3b^3}{5}$