Question

Simplify each expression:

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

Short 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-by-step solution

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 b9·b8.

As we know$a^m·a^n=a^{m+n}$

Part(a) Step 2. The given expression is b9·b8.

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  42x·4x 

As we know$a^m·a^n=a^{m+n}$

Part(b) Step 2. The given expression is  42x·4x 

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 3p5·4p

As we know$a^m·a^n=a^{m+n}$

Part(c) Step 2. The given expression is 3p5·4p

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  x6·x4·x8

As we know$a^m·a^n=a^{m+n}$

Part(d) Step 2. The given expression is  x6·x4·x8

Add the exponents, since bases are the same.

$x^6·x^4·x^8=x^{6+4+8}$

Simplifying the expression.

$x^6·x^4·x^8=x^{18}$