Question

Simplify (z 7 z -5)-2

Answer 1

The expression (z^7 z^{-5})^{-2} simplifies to 1/z^4 by applying the laws of exponents to combine and subsequently simplify the terms.

Step-by-step explanation:

To simplify the expression (z^7 z^{-5})^{-2}, we first combine the exponents of the same base by adding them. Since we're multiplying z to different powers, according to the laws of exponents, we can add the exponents:

z^7 × z^{-5} = z^{7 + (-5)}

= z^2

Now, we raise this to the power of -2:

(z^2)^{-2} = z^{2 × (-2)}

= z^{-4}

And as a final step, because negative exponents indicate the reciprocal, we can write this as:

z^{-4} = 1/z^4

So, (z^7 z^{-5})^{-2} simplifies to 1/z^4.