Q. 5.24 - Intermediate Algebra

Question

Simplify each expression:

$ⓐ x^{12}·x^4 ⓑ 10·{10}^x ⓒ 2z·6z^7 ⓓ b^5·b^9·b^5$

Step-by-Step Solution

Answer

The simplified expression of $x^{12}·x^4 =x^{16}$

The simplified expression of $10·{10}^x={10}^{1+x}$

The simplified expression of $2z·6z^7= 2z^8$

The simplified expression of $b^5·b^9·b^5=b^{19}$

Step 1. Given Information

In the given question we have to simplify each expression: 

$ⓐ x^{12}·x^4 ⓑ 10·{10}^x ⓒ 2z·6z^7 ⓓ b^5·b^9·b^5$

Part(a) Step 1. Simplifying the expression x 12 · x 4  

As we know $a^m·a^n=a^{m+n}$

Part(a) Step 2. The given expression is x 12 · x 4  

Add the exponents, since bases are the same.

$x^{12}·x^4 =x^{12+4}$

Simplifying the expression.

$x^{12}·x^4 =x^{16}$

Part(b) Step 1. Simplifying the expression 10 · 10 x

As we know $a^m·a^n=a^{m+n}$

Part(b) Step 2. The given expression is 10 · 10 x

Rewrite $a=a^1$

$10·{10}^x={10}^1·{10}^x$

Add the exponents, since bases are the same.

$10·{10}^x={10}^{1+x}$

Part(c) Step 1. Simplifying the expression   2 z · 6 z 7

As we know $a^m·a^n=a^{m+n}$

Part(c) Step 2. The given expression is   2 z · 6 z 7

Rewrite $a=a^1$

$2z·6z^7= 2z^1·6z^7$

Use the Commutative Property and use the Product Property

$2z·6z^7= 2·6z^{1+7}$

Simplifying the expression.

$2z·6z^7= 2z^8$

Part(d) Step 1. Simplifying the expression b 5 · b 9 · b 5

As we know $a^m·a^n=a^{m+n}$

Part(d) Step 2. The given expression is b 5 · b 9 · b 5

Add the exponents, since bases are the same.

$b^5·b^9·b^5=b^{5+9+5}$

Simplifying the expression.

$b^5·b^9·b^5=b^{19}$