Chapter 7.4, Problem 1P

a.

To determine

To write: the simplified form of expression $\frac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}$

Answer to Problem 1P

The required answer is: $y^{\frac{1}{4}}$

Explanation of Solution

Given information:

The given expression: $\frac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}$

Calculation:

  $\frac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}=y^{\frac{3}{4}-\frac{1}{2}}$

(Subtract exponents when dividing powers with the same base)

  $\begin{array}{l}=y^{\frac{3-2}{4}}\\ =y^{\frac{1}{4}}\end{array}$

(Simplify)

b.

To determine

To write: the simplified form of expression $\frac{d^{\frac{7}{2}}}{d^3}$

Answer to Problem 1P

The required answer is: $d^{\frac{1}{2}}$

Explanation of Solution

Given information:

The given expression: $\frac{d^{\frac{7}{2}}}{d^3}$

Calculation:

  $\frac{d^{\frac{7}{2}}}{d^3}=d^{\frac{7}{2}-3}$

(Subtract exponents when dividing powers with the same base)

  $\begin{array}{l}=d^{\frac{7-6}{2}}\\ =d^{\frac{1}{2}}\end{array}$

(Simplify)

c.

To determine

To write: the simplified form of expression $\frac{k^6{j}^2}{k{j}^5}$

Answer to Problem 1P

The required answer is: $\frac{k^5}{j^3}$

Explanation of Solution

Given information:

The given expression: $\frac{k^6{j}^2}{k{j}^5}$

Calculation:

  $\frac{k^6{j}^2}{k{j}^5}=k^{6-1}{j}^{2-5}$

(Subtract exponents when dividing powers with the same base)

  $\begin{array}{l}=k^5{j}^{-3}\\ =k^5\cdot \frac{1}{j^3}\end{array}$

(Rewrite using positive exponents)

  $=\frac{k^5}{j^3}$

(Simplify)

d.

To determine

To write: the simplified form of expression $\frac{a^{-3}{b}^7}{a^5{b}^2}$

Answer to Problem 1P

The required answer is: $\frac{b^5}{a^8}$

Explanation of Solution

Given information:

The given expression: $\frac{a^{-3}{b}^7}{a^5{b}^2}$

Calculation:

  $\frac{a^{-3}{b}^7}{a^5{b}^2}=a^{-3-5}{b}^{7-2}$

(Subtract exponents when dividing powers with the same base)

  $\begin{array}{l}=a^{-8}{b}^5\\ =\frac{1}{a^8}\cdot b^5\end{array}$

(Rewrite using positive exponents)

  $=\frac{b^5}{a^8}$

(Simplify)

e.

To determine

To write: the simplified form of expression $\frac{x^4{y}^{-1}{z}^8}{x^4{y}^{-5}z}$

Answer to Problem 1P

The required answer is: $\frac{k^5}{j^3}$

Explanation of Solution

Given information:

The given expression: $\frac{x^4{y}^{-1}{z}^8}{x^4{y}^{-5}z}$

Calculation:

  $\frac{x^4{y}^{-1}{z}^8}{x^4{y}^{-5}z}=x^{4-4}{y}^{-1-(-5)}{z}^{8-1}$

(Subtract exponents when dividing powers with the same base)

  $\begin{array}{l}=x^0{y}^{-1+5}{z}^7\\ =1\cdot y^4{z}^7\\ =y^4{z}^7\end{array}$

(Simplify)