Q. 83. - Intermediate Algebra

Question

In the following exercises, simplify each expression using the properties for exponents.

$ⓐ n^{19}·n^{12} ⓑ 3^x·3^6 ⓒ 7w^5·8w ⓓ a^4·a^3·a^9$

Step-by-Step Solution

Answer

The simplified form of given expression $n^{19}·n^{12}=n^{31}$

The simplified form of given expression $3^x·3^6=3^{x+6}$

The simplified form of given expression $7w^5·8w=56w^6$

The simplified form of given expression $a^4·a^3·a^9=a^{16}$

Step 1. Given Information

In the given question we have to simplify the given expression:

$ⓐ n^{19}·n^{12} ⓑ 3^x·3^6 ⓒ 7w^5·8w ⓓ a^4·a^3·a^9$

Part (a) Step 1. The given expression is n 19 · n 12

Use the Product Property, $a^m·a^n=a^{m+n}$

$n^{19}·n^{12}=n^{19+12}$

Simplify.

$n^{19}·n^{12}=n^{31}$

Part (b) Step 1. The given expression is 3 x · 3 6

Use the Product Property, $a^m·a^n=a^{m+n}$

$3^x·3^6=3^{x+6}$

Part (c) Step 1. The given expression is 7 w 5 · 8 w

$$\begin{gathered} 7w^5·8w=7w^5·8w^1 \\ 7w^5·8w=7·8·w^5·w^1 \end{gathered}$$

Use the Product Property, $a^m·a^n=a^{m+n}$

$7w^5·8w=7·8·w^{5+1}$

Simplify.

$7w^5·8w=56w^6$

Part (d) Step 1. The given expression is a 4 · a 3 · a 9

Use the Product Property, $a^m·a^n=a^{m+n}$

$a^4·a^3·a^9=a^{4+3+9}$

Simplify.

$a^4·a^3·a^9=a^{16}$