Posted by Annie on Monday, October 18, 2010 at 7:20pm.


Choose the equivalent expression(3h^-2j^3k)^2(hj^-5k^3)^-2 The signs that look like minuses are negative signs

Answers:
3h^-6j^16K^-4
9h^-2j^5j^16k^-4
9h^-6j^-4k^-4
9h^-6j^-4k^-4

Please help I'm so lost right now-Ireally don't get it- I think it might be the last one, but I'm not sure

To simplify the given expression, we need to use the properties of exponents and apply them step by step. Let's break it down:

Expression: (3h^(-2)j^(3)k)^(2)(hj^(-5)k^(3))^(-2)

1. Start by simplifying the exponents inside the parentheses. Multiply the exponents by the coefficient in front of them:
(3^2)(h^(-2*2))(j^(3*2))(k^(1*2))(h^(1*(-2)))(j^(-5*(-2)))(k^(3*(-2)))

Simplifying further:
9h^(-4)j^(6)k^(2)h^(-2)j^(10)k^(-6)

2. We can now combine the like terms:
9h^(-4 - 2)j^(6 + 10)k^(2 - 6)

Simplifying:
9h^(-6)j^(16)k^(-4)

So the correct answer is 9h^(-6)j^(16)k^(-4).

It should have read please check-

I am going to leave a space between factors for easier reading

(3h^-2 j^3 k)^2(h j^-5 k^3)^-2
= (9 h^-4 j^6)/(h^2 j^-10 k^6)
= 9 h^-6 j^16 k^-4

Thank you-I see where I made the mistake on the "j"

did you also notice that none of the given answers are correct ?