Chapter 6.2, Problem 40E

To determine

To simplify: the expression provided in the question

Answer to Problem 40E

  $\frac{2x^4·x^3}{6x^6}=\frac{x}{3}$

Explanation of Solution

Given information: consider the expression provided in the question,

  $\frac{2x^4·x^3}{6x^6}$

Calculation:

Use the product of powers property, that is, by multiplying the base, the powers of the two numbers multiplied gets added,

  $\frac{2x^{4+3}}{6x^6}=\frac{2x^7}{6x^6}$

Use the quotient of power property, that is, by dividing the base, the powers of the two numbers divided gets subtracted,

  $\frac{2x^{7-6}}{6}=\frac{2x}{6}$

Divide the numerator and denominator with 2,

  $\frac{2x÷2}{6÷2}=\frac{x}{3}$

Hence, $\frac{2x^4·x^3}{6x^6}=\frac{x}{3}$