Grade 11 U Math help NAO PLOX.

[pkingworrier]

Okay, sooo... This is a math assignment due... tomorrow
I don't understand it. I don't want just the answers, I want an explanation to these questions:

1) What restrictions are there on the value of x ^ -1/2? Are these restrictions different for x ^ 1/2? Explain.

2. Evaluate. Express answers in rational form.
a) (49/81) ^ 1/2
b) *square root* 100/121
c)((-125)^1/3)^-3


that's all for now :/

 

[Weasel2013]

Okay, sooo... This is a math assignment due... tomorrow
I don't understand it. I don't want just the answers, I want an explanation to these questions:

1) What restrictions are there on the value of x ^ -1/2? Are these restrictions different for x ^ 1/2? Explain.

2. Evaluate. Express answers in rational form.
a) (49/81) ^ 1/2
b) *square root* 100/121
c)((-125)^1/3)^-3


that's all for now :/

1) No idea what the hell restrictions are. But X ^ -1/2 can be any sort of number, including imaginary, or +/-, whereas x ^ 1/2 can only be positive or negative.

2)
a) Use a calculator.
b) Long decimal, don't have the time right now.
c) Use a calculator.

 

[Abel37]

1) X can not be zero, this would make 0 be in the denominator and you can not divide by zero. x ^ (1/2) has no restrictions.
2. Evaluate. Express answers in rational form.
a) (49/81) ^ 1/2 = √ 49/√ 81 = 7/9
b) *square root* 100/121 = √ 100/√ 121 = 10/11
c)((-125)^1/3)^-3 = (-125)^(1/3) = (-5)^-3 = -1/125

 

[pkingworrier]

1) No idea what the hell restrictions are. But X ^ -1/2 can be any sort of number, including imaginary, or +/-, whereas x ^ 1/2 can only be positive or negative.

2)
a) Use a calculator.
b) Long decimal, don't have the time right now.
c) Use a calculator.

I don't understand how to do it though :/

 

[Abel37]

When raising a number by a fraction the numerator is the number you raise it to, and the denominator is how you root it.

Example - 125^(1/3) = ³√ 125 = 5
Example - 5^(3/1) = 125

When you raise a number by a negative number you switch the numerator with the denominator.

Example = 5^-2 = 1/25
Example = (5/10)^-2 = 100/25 = 4

 

[pkingworrier]

When raising a number by a fraction the numerator is the number you raise it to, and the denominator is how you root it.

Example - 125^(1/3) = ³√ 125 = 5
Example - 5^(3/1) = 125

When you raise a number by a negative number you switch the numerator with the denominator.

Example = 5^-2 = 1/25
Example = (5/10)^-2 = 100/25 = 4

You've helped me.. like A LOT. Thanks, you just saved about 5% of my assignments mark ;P

 

[Weasel2013]

Abel37 is correct...pking; you can find square root symbols online. I was confused about what the problem actually was, b isn't a decimal then if you're square rooting the whole fraction and not just the first number. And for a calculator, include parantheses exactly as they're shown in the problem, and it will do the order of operations for you.

I agree that x cannot be zero...but I feel my answer had further reasoning..if you only had one line to answer that question in go with Abel's, but if you need to fill up space mix ours.

 

[pkingworrier]

Alright... I only really need to answer it with little reasoning as long as I can explain what I did... I solved a) myself but felt the way I did it was wrong. Now I see it's right. Why is it that when it's ^1/2 I can just do the square root? :s

 

[DtheK]

Alright... I only really need to answer it with little reasoning as long as I can explain what I did... I solved a) myself but felt the way I did it was wrong. Now I see it's right. Why is it that when it's ^1/2 I can just do the square root? :s

Not sure what the "correct" way to explain it would be, but here's how I see it.

Say you have a number X. Take X^(1/2), then square that quantity. You get (X^(1/2)^2), which simplifies to just X. What quantity would X^(1/2) be if when we square it, we get X? Obviously the square root of X. So taking a number to the 1/2 power = taking the square root of it.

 

[pkingworrier]

Ahhh, I see. So essentially, 1/2= square root... Much like 2/1 is =1?

 

[Abel37]

Ahhh, I see. So essentially, 1/2= square root... Much like 2/1 is =1?

Yes, raising a number by (1/2) is getting it's square root. And no, raising a number by (2/1) is the same as raising it by 2, not 1.

 

[pkingworrier]

Yes, raising a number by (1/2) is getting it's square root. And no, raising a number by (2/1) is the same as raising it by 2, not 1.

2 is what I meant xD sorry, was distracted ...
Can you explain in detail what you did with the ((-125)^1/3)^-3? I don't get it...

 

[Abel37]

2 is what I meant xD sorry, was distracted ...
Can you explain in detail what you did with the ((-125)^1/3)^-3? I don't get it...

Alright, first, lets break down the problem.
((-125)^1/3)^-3

PEMDAS states that you do the parentheses first.
(-125)^1/3 = ³√-125

³√-125 = 5

You're now left with 5^-3

5^-3 = 1/125

 

[pkingworrier]

Ahh, I see now xD thanks.

 

[pkingworrier]

Err, "Evaluate. Express answers to three decimals"

a) -456^4/7
b) 98^0.75
c)(5/8)^5/8
d) (^5√-1000^3)

... Damn this is hard D:

 

[Koot]

Wow weasels answers are garbage, you're never supposed to use a calculator to find the decimal when there's a mathematical way to reduce and simplify it.

As for restrictions, it means the domain of the function. What values it can be. They're right as the -1/2 cannot equal 0. For the general its about anything besides 0. For 1/2 if you are only looking in the real set of numbers its just 0 and onward as negative inputs will give you the complex plane.

Err, "Evaluate. Express answers to three decimals"

a) -456^4/7
b) 98^0.75
c)(5/8)^5/8
d) (^5√-1000^3)

... Damn this is hard D:

Well here you're supposed to use a calculator because they specifically ask you to 3 decimal places. No way you can do that by hand unless you're a math genius.

 

[pkingworrier]

Do I just do 4/7 x -456? I dunno man, I'm a math retard.

 

[Abel37]

a) -456^4/7
(-456)^4 = -43237380096
-43237380096^(1/7) = -33.06804207

b) 98^0.75
98^(3/4)
98^3 = 941192
941192^1/4 = 31.1472391

c)(5/8)^5/8

5^(5/8) / 8^(5/8)
5^5 = 3125
3125^1/8 = 2.734363529

8^5 = 32768
32768^1/8 = 3.668016174

2.734363529/3.668016174 = .7454611431

d) (^5√-1000^3)
Do you mean the 5th root of -1000 raised to the third? if so:
-1000^(3/5)
-1000^(1/5) = -3.981071706
-3.981071706^3 = -63.09573445

Here is proof of the answers:

 

[Koot]

There should be the ^ button on the calculator which means exponent. Just put how you wrote it on the calculator.

 

[pkingworrier]

It still makes no sense :/ like why only do -456^4? What about the 7? And how did you get 1/7? And how come when I do -43237380096 x 1/7 it gives me a HUGE number, like 6885734743 or something?