Chapter 1.4, Problem 24PPE

To determine

To Evaluate: The expression $\frac{c^2}{b^2}+\frac{b^2}{a^2}$

Answer to Problem 24PPE

  $\frac{c^2}{b^2}+\frac{b^2}{a^2}=16\frac{1}{4}$

Explanation of Solution

Given information:

The expression $\frac{c^2}{b^2}+\frac{b^2}{a^2}$ and value of $a=8,b=4\&c=16$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times}\text{.}$

BODMAS rule

Calculation:

The given expression is $\frac{c^2}{b^2}+\frac{b^2}{a^2}$

Putting the values of $a=8,b=4\&c=16$ in the expression

  $\begin{array}{l}\frac{c^2}{b^2}+\frac{b^2}{a^2}=\frac{{16}^2}{4^2}+\frac{4^2}{8^2}\\ {\text{Evaluate the powers 16}}^2\&4^2\text{ in numerator}\\ \frac{c^2}{b^2}+\frac{b^2}{a^2}=\frac{256}{4^2}+\frac{16}{8^2}\\ {\text{Evaluate the powers 4}}^2\&8^2\text{ in denominator}\\ \frac{c^2}{b^2}+\frac{b^2}{a^2}=\frac{256}{16}+\frac{16}{64}\\ \text{on simplifying}\\ \frac{c^2}{b^2}+\frac{b^2}{a^2}=16+\frac{1}{4}\\ \frac{c^2}{b^2}+\frac{b^2}{a^2}=16\frac{1}{4}\end{array}$

Conclusion:

  $\frac{c^2}{b^2}+\frac{b^2}{a^2}=16\frac{1}{4}$