Question

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

$ⓐq^{27}·q^{15}ⓑ5^x·5^{4x}ⓒ9u^{41}·7u^{53}ⓓc^5·c^{11}·c^2$

Short answer

The simplified form of given expression$q^{27}·q^{15}=q^{42}$

The simplified form of given expression$5^x·5^{4x}=5^{5x}$

The simplified form of given expression$9u^{41}·7u^{53}=63u^{94}$

The simplified form of given expression$c^5·c^{11}·c^2=c^{18}$

Step-by-step solution

Step 1. Given Information 

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

$ⓐq^{27}·q^{15}ⓑ5^x·5^{4x}ⓒ9u^{41}·7u^{53}ⓓc^5·c^{11}·c^2$

Part (a) Step 1. The given expression is q27·q15

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

$q^{27}·q^{15}=q^{27+15}$

Simplify.

$q^{27}·q^{15}=q^{42}$

Part (b) Step 1. The given expression is 5x·54x

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

$5^x·5^{4x}=5^{x+4x}$

Simplify.

$5^x·5^{4x}=5^{5x}$

Part (c) Step 1. The given expression is  9u41·7u53

$9u^{41}·7u^{53}=9·7·u^{41}·u^{53}$

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

$9u^{41}·7u^{53}=9·7·u^{41+53}$

Simplify.

$9u^{41}·7u^{53}=63u^{94}$

Part (d) Step 1. The given expression is c5·c11·c2

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

$c^5·c^{11}·c^2=c^{5+11+2}$

Simplify.

$c^5·c^{11}·c^2=c^{18}$