48.0k views
3 votes
Which expression is equivalent to 3 square root of x to the power of 10

Which expression is equivalent to 3 square root of x to the power of 10-example-1
User Wizardzeb
by
8.1k points

1 Answer

2 votes

The trick of the problem is to change the question into: Which expression is equivalent to x^10? Because the 3 square root is not changed in any sense. Now, we need to remember what could be with an expression like x^10. First, one can't add numbers without care (sloppily). For instance, if our x were 1,


x^(10)=(1)^(10)=1\\e3(1)=3\cdot x^(10)

Thus, we must discard the second option. We can discard the third option too, for sum and product are really different operations. Finally, without discard the first option, I want to say that we can "separate" the exponent of an expression through the product. This could sound strange, but it just means


x^(a+b)=x^a\cdot x^b

With this property in mind, we can say that


x^(10)=x^(9+1)=x^9\cdot x^1=x^9\cdot x

Thus, our answer is the last option.

User Oposum
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.