Fully simplify (z^3)^0\cdotz^6

= 1 * z^6

= z^6

To fully simplify the expression (z^3)^0 * z^6, we can use the properties of exponents.

First, let's consider the exponent of (z^3)^0. Any number raised to the power of 0 is equal to 1. So, (z^3)^0 = 1.

Now, let's simplify the remaining portion of the expression, z^6.

To multiply two terms with the same base, we add their exponents. So, z^6 can be written as z^(3+3) = z^3 * z^3.

Putting it all together, (z^3)^0 * z^6 simplifies to 1 * z^3 * z^3 = z^3 * z^3 = z^(3+3) = z^6.

Therefore, the fully simplified form of (z^3)^0 * z^6 is z^6.

To fully simplify the expression, let's break it down step by step.

First, recall that any number raised to the power of 0 is equal to 1. So, (z^3)^0 equals 1.

Next, we can apply the product rule of exponents, which states that when you multiply two terms with the same base, you can add their exponents. In this case, we have z^0 multiplied by z^6.

Since z^0 equals 1, we can simplify the expression to 1 * z^6, which is simply z^6.

So, the fully simplified expression is z^6.