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### Course: Algebra (all content)>Unit 11

Lesson 7: Simplifying radicals (higher-index roots)

# Simplifying cube root expressions (two variables)

Sal simplifies ∛(125x⁶y³) as 5x²y. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• what do you do when the whole number is not a perfect cube number?
• you would up with an answer of something like 54.09. it depends on what the question asks you to to do.
• I need to find the topic of powers of powers (exponents) or taking a power to a power, could someone help me find a video where Sal explains that please?
Much appreciated.
• Why does Sal change it to ³√ to ^⅓?
• It is essentially the same thing.
Sal did it perhaps to show you the relations between the power and the roots.
• What is 3 to the -½ power?
• why do you factor
• So that we can manipulate all the other variables in an equation to find the value of a missing variable.
• I am asked to simplify using laws of exponents and write the final answer in exponential form. What does that mean ? how do i do that?
• you will be given an equation or expression with lots of exponents in, that means it has lots of things to the power of other things. when you see two exponents timesed together like 2^3 * 2^4 you may simply add the two exponents giving 2^7. if you send me the question I can explain how to do that particular one
• at you write and say that we have to think that the cube root is the same thing as powering a number by 1/3. Do we have to do it or can we just factorize from the cube root?
(1 vote)
• Well, you can solve something raised to the 1/3 by taking the cube root directly. It's just about understanding the root relationship to fractions as it will become even more important when it becomes things like 2/3, or properties that can't be directly found by taking a root.
• what is (33/17) whole the power of -15 divided by (33/170 whole to the power of 8 = (33/17) whole to the power of 4x-9 find x ?
(1 vote)
• If you have like bases, you can set your exponents equal. So if((33/17)^-15)/(33/17)^8 =(33/17)^4x-9, THEN (-15/8)=4x-9, so multiply by 8 and -15=32x-72, now add 72 to each side, and -57 = 32x, and -1.78125 = x
(1 vote)
• 7/x + 1/4 = 9/x
(1 vote)
• 1) Subtract 7/x from both sides: 1/4 = 2/x
2) At this point, you have 2 options. You have a proportion so you can cross multiply. Or, you can use the LCD = 4x and multiply both sides by the LCD. You will get:
x = 8

Hope this helps.