Chapter 4.5, Problem 56E

To determine

To simplify the following expression $\frac{6z^9·8z^3}{27z^2}$

Answer to Problem 56E

  $\frac{16z^{10}}{9}$

Explanation of Solution

Given information : $\frac{6z^9·8z^3}{27z^2}$

This answer shall be derived using the product of powers rule, wherein the exponents of a common base can be added during multiplication and subtracted during division.

Calculation:

Given, $\frac{6z^9·8z^3}{27z^2}$

  $=\frac{2\times 3\times 2^3\times z^9\times z^3}{3^3\times z^2}$ Here, it’s written as6 as $2*3$ , 8 as $2^3$ and 27 as $3^3$

  $=\frac{2^{1+3}\times z^{9+3-2}}{3^{3-1}}$ Here, the exponents of the bases ‘z’, 2 and 3 are adjusted.

  $=\frac{2^4\times z^{10}}{3^2}$

  $=\frac{16z^{10}}{9}$ This is the simplified expression