Question

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

$ⓐx^4·x^2ⓑ8^{9x}·8^3ⓒ3z^{25}·5z^8ⓓy·y^3·y^5$

Short answer

The simplified form of given expression$x^4·x^2=x^6$

The simplified form of given expression$8^{9x}·8^3=8^{9x+3}$

The simplified form of given expression$3z^{25}·5z^8=15z^{33}$

The simplified form of given expression$y·y^3·y^5=y^9$

Step-by-step solution

Step 1. Given Information 

In the given question we have to simplify the given expression:
$ⓐx^4·x^2ⓑ8^{9x}·8^3ⓒ3z^{25}·5z^8ⓓy·y^3·y^5$

Part (a) Step 1. The given expression is x4·x2

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

$x^4·x^2=x^{4+2}$

Simplify.

$x^4·x^2=x^6$

Part (b) Step 1. The given expression is 89x·83

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

$8^{9x}·8^3=8^{9x+3}$

Part (c) Step 1. The given expression is 3z25·5z8

$3z^{25}·5z^8=3·5·z^{25}·z^8$

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

$3z^{25}·5z^8=15·z^{25+8}$

Simplify.

$3z^{25}·5z^8=15z^{33}$

Part (d) Step 1. The given expression is y·y3·y5

$y·y^3·y^5=y^1·y^3·y^5$

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

$y·y^3·y^5=y^{1+3+5}$

Simplify.

$y·y^3·y^5=y^9$