Help on question about direct and inverse proportions

[Eleonora]

I worked out that z=18/√y
But I know that the answer should be z=18y^-1/2
Are the two equations the same? If yes, why?

Thank you in advance : )

I noticed the dot on my account is green, what does it mean?

 

[Deleted member 4993]

View attachment 20776

I worked out that z=18/√y
But I know that the answer should be z=18y^-1/2
Are the two equations the same? If yes, why?

Thank you in advance : )

I noticed the dot on my account is green, what does it mean?

Those are same:

z = 18/√y = 18y^(-1/2)

I am assuming that you know:

√y = y^(1/2)

Then apply "laws of exponentiation", which states:

1/a^m = a^(-m)

 

[Eleonora]

I have actually never heard of the law of exponentation. Could you explain it to me? This maths is a few classes above mine.
Thank you so much

 

[Deleted member 4993]

I have actually never heard of the law of exponentiation. Could you explain it to me? This maths is a few classes above mine. Thank you so much

Do a google search with keywords:

laws of exponentiation

You will find >100,000 sites ready to explain to you through video or text.

Please go through some of those and tell us what you found. We can then explain further - if needed.

 

[Eleonora]

Ok, thank you. I will let you know. Have a nice day

 

[Steven G]

By DEFINITION x^-1 = 1/x. Also (x^a)^b=x^ab and (a/b)ⁿ = aⁿ/bⁿ

Then x^-n = (x^-1)ⁿ=(1/x)ⁿ = 1ⁿ/xⁿ = 1/xⁿ

 

[mmm4444bot]

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[Otis]

I have actually never heard of the law of [exponentiation] …

Hi Eleonora. Some people call them laws; other people call them properties. Your textbook ought to list them.



Note: In the second property above, they ought to have specified that 0⁰ is not defined. Even so, students may see 0⁰ defined as 1 in precalculus (or later).

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[Eleonora]

Thank you much everyone for the kind and detailed answers!! I understand now. Have a great day!