Q. 5.36 - Intermediate Algebra

Question

Simplify each expression:

$ⓐ {\left(z^6\right)}^9 ⓑ {\left(3^7\right)}^7 ⓒ {\left(q^4\right)}^5 {\left(q^3\right)}^3$

Step-by-Step Solution

Answer

The simplified expression of ${\left(z^6\right)}^9=z^{54}$

The simplified expression of ${\left(3^7\right)}^7=3^{49}$

The simplified expression of ${\left(q^4\right)}^5 {\left(q^3\right)}^3=q^{29}$

Step 1. Given Information

In the given question we have to simplify each expression: 

$ⓐ {\left(z^6\right)}^9 ⓑ {\left(3^7\right)}^7 ⓒ {\left(q^4\right)}^5 {\left(q^3\right)}^3$

Part (a) Step 1. The given expression is ( z 6 ) 9  

Use the Power Property, ${\left(a^m\right)}^n=a^{m·n}$

${\left(z^6\right)}^9=z^{6·9}$

Simplifying

${\left(z^6\right)}^9=z^{54}$

Part (b) Step 1. The given expression is ( 3 7 ) 7

Use the Power Property, ${\left(a^m\right)}^n=a^{m·n}$

${\left(3^7\right)}^7=3^{7·7}$

Simplifying

${\left(3^7\right)}^7=3^{49}$

Part (c) Step 1. The given expression is ( q 4 ) 5   ( q 3 ) 3

Use the Power Property, ${\left(a^m\right)}^n=a^{m·n}$

${\left(q^4\right)}^5 {\left(q^3\right)}^3=\left(q^{4·5}\right)(q^{3·3})$

Simplifying

${\left(q^4\right)}^5 {\left(q^3\right)}^3=\left(q^{20}\right)(q^9)$

$$\begin{gathered} {\left(q^4\right)}^5 {\left(q^3\right)}^3=q^{20+9} \\ {\left(q^4\right)}^5 {\left(q^3\right)}^3=q^{29} \end{gathered}$$