help with solving this equation

\[2x ^{1/4}= 64/x\]

ARe we solving for x?

yes m8

divide by 2. leaves you with x^(1/4) = 32/x times both sides by x^(4/4) * x^(1/4) = 32 when you multiply like terms, that gets you x^(5/4) = 32 take both sides to ^(4/5) x=32^(4/5) x=16

Haha sorry I am bit slow when typing math problems.

where do you get the 4/4

x^(4/4) * x^(1/4) = 32

when you multiply exponential terms you add the exponent. So...1/4+1=1/4+4/4=5/4

4/4 = 1, and it was x^1 power. I was just finding a common denominator so you could add them together!

can you explain it lemans

\[x^{1/4}\]

You're multiplying x^1 and x^1/4 right? so when you multiply the two terms, you add their exponents. How do you add fractions together? You must find a common denominator. Right now we have 1/1 + 1/4 To find a common denominator, we change the 1/1 to 4/4 so now we can add 4/4 and 1/4 which gives us 5/4

why do i multiply it just by 1 on the left side

\[x^{1/4}=32/x\]

i thought it would be\[^{4/1} x ^{1/4 }=32/x ^{4/1}\]

to cancel out the power on the left handside

You aren't, remember you started with an x on the right side, so you multiply BOTH sides by x.

i need a video tutorial for this lol

i still dont understand

32/x. the x has a power of one and i bring it over to the left hand side

combing like terms. 32/x=32*1/x So you when muliply it out it will be x^1/4*x^1

so takink the x from 32/x to the left hand side means 1/4 becomes 5/4 bacause x has a power of 1 which is 4/4

Yes that is correct. just combing like terms and in order for this to happen you needed to find a common den, so you can add the exponents.

is the ex ponent x

so how fo you get 16 from x^5/4 = 32

2x^1/4=64/x 2x^1/4=64*1/x x^1/4=32*1/x x^1*x^1/4=32 x^4/4*x^1/4=32 x^5/4=32 x=32^4/5 x=16

no x is the variable. The exponents are 1 and 1/4

I tried to write out every step

what do i do to the 32 then

combing like terms so we want our variables on one side and constants on the other. the part that makes this equation hard are the fractions. so lets look at it without fractions 2x^4=64/x 2x^4=64*1/x now we want to isolate the x's, so get rid of the 2 first x^4=32*1/x now combine x's, by multiplying by the reciprocal of 1/x x*x^4=32 x^5=32 \[x =\sqrt[5]{32}\]

THat is what you are doing to the original problem but with fractions in the exponent.

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