Q. 5.35 - Intermediate Algebra

Question

Simplify each expression:

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

Step-by-Step Solution

Answer

The simplified expression of ${\left(b^7\right)}^5=b^{35}$

The simplified expression of ${\left(5^4\right)}^3=5^{12}$

The simplified expression of ${\left(a^4\right)}^5 {\left(a^7\right)}^4=a^{48}$

Step 1. Given Information

In the given question we have to simplify each expression:

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

Part (a) Step 1. The given expression is ( b 7 ) 5

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

${\left(b^7\right)}^5=b^{7·5}$

Simplifying

${\left(b^7\right)}^5=b^{35}$

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

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

${\left(5^4\right)}^3=5^{4·3}$

Simplifying

${\left(5^4\right)}^3=5^{12}$

Part (c) Step 1. The given expression is ( a 4 ) 5   ( a 7 ) 4

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

${\left(a^4\right)}^5 {\left(a^7\right)}^4=(a^{4·5}\left)\right(a^{7·4})$

Simplifying

${\left(a^4\right)}^5 {\left(a^7\right)}^4=a^{20}{a}^{28}$

$$\begin{gathered} {\left(a^4\right)}^5 {\left(a^7\right)}^4=a^{20+28} \\ {\left(a^4\right)}^5 {\left(a^7\right)}^4=a^{48} \end{gathered}$$