Chapter 4, Problem 17MCQ

To determine

To write the fraction in simplest form $\frac{15b}{39b^4}$

Answer to Problem 17MCQ

  $\frac{5}{13b^3}$

Explanation of Solution

Given information:

Expression $\frac{15b}{39b^4}$

Formula Used: Factorization, Quotient Rule & Negative Exponent Rule

Calculation:

Here, break both the numerator & denominator into its factors respectively.

So, 15b may be written as $3\times 5\times b$

And $39b^4$ may be written as $13\times 3\times b^4$

The fraction is revised as follows-

  $\frac{15b}{39b^4}=\frac{3\times 5\times b}{13\times 3\times b^4}$

As can see that 3 is available in both numerator & denominator. Also, since the base ‘b’ is same, apply the quotient rule. So have-

  $\frac{3\times 5\times b}{13\times 3\times b^4}=\frac{5b}{13\times b^4}=\frac{5b^{1-4}}{13}$

apply the negative exponent rule here, and reverse the numerator to denominator for ‘a’.

Hence,

  $\frac{5b^{-3}}{13}=\frac{5}{13b^3}$

Conclusion-

  $\frac{5}{13b^3}$