Chapter 7.1, Problem 44PPS

To determine

To Simplify: The expression ${\left(5k^{2}m\right)}^3{\left[{\left(4k{m}^4\right)}^2\right]}^2$

Answer to Problem 44PPS

The required answer is $32000k^{10}{m}^{19}$ .

Explanation of Solution

Given information:

The expression ${\left(5k^{2}m\right)}^3{\left[{\left(4k{m}^4\right)}^2\right]}^2$

Calculation:

  ${\left(5k^{2}m\right)}^3{\left[{\left(4k{m}^4\right)}^2\right]}^2$

  $={\left(5k^{2}m\right)}^3{\left(4k{m}^4\right)}^4$

(Power of a power)

  $=5^3{\left(k^2\right)}^3{m}^3{4}^4{k}^4{\left(m^4\right)}^4$

(Power of a product)

  $=5^3{k}^6{m}^3{4}^4{k}^4{m}^{16}$

(Power of a power)

  $=5^3\cdot 4^4{k}^6{k}^4{m}^3{m}^{16}$

(Commutative)

  $=5^3\cdot 4^4{k}^{10}{m}^{19}$

(Product of powers)

  $=32000k^{10}{m}^{19}$

(Simplify)