simplify (assume the variables represent positive values):
\sqrt{8z^{8}}/\sqrt{2}
To simplify this expression, we can first rewrite the radicand as a power of 2:
\sqrt{8z^{8}} = \sqrt{(2^3)(z^8)} = \sqrt{(2^3)(z^4)^2} = \sqrt{(2^3)} \cdot \sqrt{(z^4)^2} = 2\cdot z^4.
Now, we can rewrite the original expression as:
\sqrt{8z^{8}}/\sqrt{2} = (2\cdot z^4)/\sqrt{2}.
We can simplify further by rationalizing the denominator. Multiplying the numerator and denominator by the conjugate of the denominator (√2), we get:
[(2\cdot z^4)/\sqrt{2}] * [\sqrt{2}/\sqrt{2}] = (2z^4\sqrt{2})/2 = z^4\sqrt{2}.
Therefore, the simplified expression is z^4√2.