Chapter SH, Problem 7.7EP

To determine

To simplify expression

  $\frac{2a^{-1}{b}^{-2}{c}^{-3}}{7a^2{b}^3{c}^4{d}^{-5}}$ .

Answer to Problem 7.7EP

  $\frac{2d^5}{7a^3{b}^5{c}^7}$

Explanation of Solution

Given information:

Expression

  $\frac{2a^{-1}{b}^{-2}{c}^{-3}}{7a^2{b}^3{c}^4{d}^{-5}}$

Calculation:

  $\frac{2a^{-1}{b}^{-2}{c}^{-3}}{7a^2{b}^3{c}^4{d}^{-5}}$

Combining like terms

  $=\frac{2}{7}\times \frac{a^{-1}}{a^2}\times \frac{b^{-2}}{b^3}\times \frac{c^{-3}}{c^4}\times \frac{1}{d^{-5}}$

Using exponent rules to get simplification,

  $=\frac{2}{7}\times \frac{1}{a^{2+1}}\times \frac{1}{b^{3+2}}\times \frac{1}{c^{4+3}}\times d^5$

On solving,

  $=\frac{2d^5}{7a^3{b}^5{c}^7}$