94.5k views
4 votes
Pleeeeeeeeeeeeeeeeas FAST !!!!! i need help if a/b = (-7/9)^8 / (-7/9)^6 find the value of (a/b)^2.

User Hroest
by
8.6k points

1 Answer

11 votes

Answer:

(-7/9)^4 = 2401/6561

Explanation:

The rules of exponents apply.

(a^b)/(a^c) = a^(b-c) . . . . . quotient rule

(a^b)^c = a^(bc) . . . . . . . . power rule

__

value of a/b

The first rule of exponents shown above helps us find the value of a/b.


(a)/(b)=(\left((-7)/(9)\right)^8)/(\left((-7)/(9)\right)^6)=\left((-7)/(9)\right)^(8-6)=\left((-7)/(9)\right)^2

value of (a/b)^2

The second rule of exponents shown above tells us how to find the square.


\left((a)/(b)\right)^2=\left(\left((-7)/(9)\right)^2\right)^2=\left((-7)/(9)\right)^(2*2)\\\\\boxed{\left((a)/(b)\right)^2=\left((-7)/(9)\right)^4=(2401)/(6561)}

_____

Additional comment

Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.

User Inderjit
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.