Chapter 4, Problem 16MCQ

To determine

To write the fraction in simplest form $\frac{32a}{8a^2}$

Answer to Problem 16MCQ

  $\frac{4}{a}$

Explanation of Solution

Given information:

Expression $\frac{32a}{8a^2}$

Formula Used: Factorization, Quotient Rule & Negative Exponent Rule

Calculation:

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

So, 32a may be written as $4\times 8\times a^1$

And 81 may be written as $8\times a^2$

The fraction is revised as follows-

  $\frac{32a}{8a^2}=\frac{4\times 8\times a^1}{8\times a^2}$

As can see that 8 is available in both numerator & denominator. Also, since the base ‘a’ is same, apply the quotient rule. So have-

  $\frac{4\times 8\times a^1}{8\times a^2}=4a^{1-2}$

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

Hence,

  $4a^{-1}=\frac{4}{a}$

Conclusion-

  $\frac{4}{a}$