Question

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

Answer 1

(-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

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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)}`

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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.