Chapter 4.6, Problem 44E

To determine

To find the quotient of $\frac{{\left(0.4\right)}^{-2}}{{\left(0.4\right)}^6}$ using positive exponents.

Answer to Problem 44E

  ${\left(\frac{5}{2}\right)}^8$

Explanation of Solution

Given information: $\frac{{\left(0.4\right)}^{-2}}{{\left(0.4\right)}^6}$

Formula used:The product of powers rule.

Calculation:

  $\frac{{\left(0.4\right)}^{-2}}{{\left(0.4\right)}^6}$

Hence it becomes

  $={\left(0.4\right)}^{-2-6}$ Using product of powers

  $={\left(\frac{4}{10}\right)}^{-8}$ Here the decimal is converted to a fraction.

  $={\left(\frac{2}{5}\right)}^{-8}$ Here, divide the numerator and the denominator by 2.

  $={\left(\frac{5}{2}\right)}^8$ Since the exponent has a negative value, interchange the numerator and the denominator. This has the positive exponents.