Simplify the expression assume all variables are positive?

What is that number? \sqrt{2} is already in terms of \sqrt{2}, so you are done.In summary, the conversation discusses three math problems: finding the cube root of a negative number, simplifying a fraction with negative exponents, and combining two radical expressions into one. The first problem can be solved by breaking down the numbers into smaller factors, the second problem involves using exponent rules to eliminate the negative exponent, and the third problem requires finding a common radical to combine the expressions.
  • #1
chris4434
2
0
I have three math problems that I am unsure of how to do. could someone please help thanks.

[tex]\sqrt[3]{-8x^3y^3z^3}[/tex]

[tex]({4xy^-1}/{16xy^2})[/tex]

[tex]\sqrt{98}+\sqrt{2}[/tex]
 
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  • #2
chris4434 said:
I have three math problems that I am unsure of how to do. could someone please help thanks.

[tex]\sqrt[3]{-8x^3y^3z^3}[/tex]

[tex]({4xy^-1}/{16xy^2})[/tex]

[tex]\sqrt{98}+\sqrt{2}[/tex]

Well for the first one you have the cube roots of 3 numbers which have been cubed so what do you think you should do?

For the second I'm not entirely sure what the expression is supposed to be but the only thing I can think of is to expres it without the negative exponent.

For the third the two radicals need to be in terms of a common radical so see if you can figure out to make [tex]\sqrt{98}[/tex] into some number times the square root of 2.
 
  • #3
chris4434 said:
I have three math problems that I am unsure of how to do. could someone please help thanks.

[tex]\sqrt[3]{-8x^3y^3z^3}[/tex]
What is [itex]\sqrt[3]{-8}[/itex]?
What is [itex]\sqrt[3]{x^3}[/itex]?


[tex]({4xy^{-1}}/{16xy^2})[/tex]
What is [itex]\frac{4}{16}[/itex]?
You have an "x" in both numerator and denominator. What can you do with that?
What does a -1 power mean?

[tex]\sqrt{98}+\sqrt{2}[/tex]
98= 2(?)
 

What does it mean to "simplify the expression"?

Simplifying an expression means to rewrite it in a more concise and simplified form by combining like terms, factoring, and using other mathematical operations.

What does it mean to "assume all variables are positive"?

This means that when simplifying the expression, you can assume that all variables in the expression have positive values. This allows you to eliminate the use of absolute value signs and simplifies the overall process.

Why is it important to assume all variables are positive when simplifying an expression?

Assuming all variables are positive allows for a more streamlined and simplified process when simplifying an expression. It also helps to avoid confusion and errors that may occur when dealing with negative values.

What are some common techniques used to simplify expressions?

Some common techniques used to simplify expressions include combining like terms, factoring, using the distributive property, and simplifying fractions.

How do I know if I have simplified an expression correctly?

To ensure that an expression has been simplified correctly, you can check by expanding the simplified expression and comparing it to the original expression. If they are equivalent, then you have simplified the expression correctly.

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