Q. 5.23 - Intermediate Algebra

Question

Simplify each expression:

$ⓐ b^9·b^8 ⓑ 4^{2x}·4^x ⓒ 3p^5·4p ⓓ x^6·x^4·x^8$

Step-by-Step Solution

Answer

The simplified expression of $b^9·b^8=b^{17}$.

The simplified expression of $4^{2x}·4^x = 4^{3x}$

The simplified expression of $3p^5·4p=12p^6$

The simplified expression of $x^6·x^4·x^8= x^{18}$

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ b^9·b^8 ⓑ 4^{2x}·4^x ⓒ 3p^5·4p ⓓ x^6·x^4·x^8$

Part(a) Step 1. Simplifying the expression b 9 · b 8 .

As we know $a^m·a^n=a^{m+n}$

Part(a) Step 2. The given expression is b 9 · b 8 .

Add the exponents, since bases are the same.

$b^9·b^8=b^{9+8}$

Simplifying the expression.

$b^9·b^8=b^{17}$

Part(b) Step 1. Simplifying the expression   4 2 x · 4 x  

As we know $a^m·a^n=a^{m+n}$

Part(b) Step 2. The given expression is   4 2 x · 4 x  

Add the exponents, since bases are the same.

$4^{2x}·4^x = 4^{2x+x}$

Simplifying the expression.

$4^{2x}·4^x = 4^{3x}$

Part(c) Step 1. Simplifying the expression 3 p 5 · 4 p

As we know $a^m·a^n=a^{m+n}$

Part(c) Step 2. The given expression is 3 p 5 · 4 p

Rewrite, $a = a^1$

$3p^5·4p=3p^5·4p^1$

Use the Commutative Property and use the Product Property

$$\begin{gathered} 3p^5·4p=3·4·p^5·p^1 \\ 3p^5·4p=3·4·p^{5+1} \end{gathered}$$

Simplifying the expression.

$3p^5·4p=12p^6$

Part(d) Step 1. Simplifying the expression   x 6 · x 4 · x 8

As we know $a^m·a^n=a^{m+n}$

Part(d) Step 2. The given expression is   x 6 · x 4 · x 8

Add the exponents, since bases are the same.

$x^6·x^4·x^8= x^{6+4+8}$

Simplifying the expression.

$x^6·x^4·x^8= x^{18}$