Am I doing these Math problems right?

Question

(81/10000)^-3/4 and I got 1000/27 Answer.
-(36/25)^ 3/2 and I got -216/125 answer
Square root of (-12)^2 and I got 12 answer
Square root of -(10)^2 and I got no solution

Thank you help is really appreciated.

thanks guys and I am talking real numbers only.

Answer 1

The first one is right. The fourth root of 10,000 is 10, and the fourth root of 81 is 3, take the reciprocal and cube to get 1,000/27.

The second is right. Unary minus binds in math lower than exponentiation (in some programming languages it is higher, so I was confused at first). the square root is 6/5, and that cubed is 216/125, perform the negation and it's the same as your answer.

The third is twelve, though square roots are in some contexts treated as "plus OR minus" (i.e., sqrt(144) = +/- 12) ).

The fourth is correct. You can't take the square root of -100 unless you're using complex numbers.

Answer 2

Boy, are you ever going to stir up a hornet's nest with this!
(81/10000)^-3/4 means 1/ (81/10000)^3/4
in English, 1 divided by the 4th root of (81/10000) cubed
= 1/(3/10)^3, =1/ 27/1000, or 1000/27. You are right.

-(36/25)^3/2 is -(6/5)^3, is (-1) (6/5)^3. We do bracket work first, so it's (-1)(6/5)^3= (-1) (216/125)
=-216/125 Again you are right

rt(-12)^2= rt 144, = + 12 0r -12. Here's where the fighting starts. I was taught that the sq rt of a number is ALWAYS + or -, and you have to sort out by various means if both answers can be used. This still makes sense to me, so I'd say your answer is partly right. After all, -12 X -12 =+ 144, doesn't it?

-(10)^2 = (-1)(10)^2, = (-1)(100), =-100. This one is the most troublesome.
I agree with you, one cannot take the sq rt of a negative number. Unless.
If you write this as (-1)(100), the answer is sqrt(-1)
times sqrt(100) = sqrt(-1)(+ or - 10). This enters the realm of complex numbers, where sqrt(-1) is given the symbol i . A whole new world!. At your present level of math, I agree with your answer.

I wish you good luck in your math.

Answer 3

(81/10000)^(-3/4) =

(3^4/10^4)^(-3/4) =

(10^4/3^4)^(3/4) =

(10^12/3^12)^(1/4) =

10^3/3^3 =

1000/27 ...........AGREED!

-(36/25)^ (3/2) =

- (6^2/5^2)^(3/2) =

- (6^6/5^6)^(1/2) =

- (6^3/5^3) =

- 216/125...........AGREED!

Square root of (-12)^2 = 12...........AGREED!

Square root of -(10)^2 - NO REAL SOLUTION - ...........AGREED!

Nice work!

Answer 4

yes you are right,but this is an easy way & will help you in long run
1)(81/10000)^-3/4
(10000/81)^3/4
(10^4/3^4)^3/4
(10/3)^4(3/4)
(10/3)^3
1000/27
2)-(36/25)^3/2
-(6^2/5^2)^3/2
-(6/5)^2(3/2)
-(6/5)^3
-216/125
3) sq rt(-12)^2
sq rt (144)
12
4)sq rt{-(10)^2}
sq rt{-100}
NO SOLUTION

Answer 5

I don't think second one has a real solution. The other three look correct.

Answer 6

I want to thank you for asking this question. I always have trouble with Radicals too and I have a test Monday!

Answer 7

Yep, they are all correct, unless your counting imaginary numbers, which the last one would be.
But otherwise, they are all correct.

Answer 8

Yeah they are all correct. You could've just checked with a calculator.