Simplify the given expression, using only positive exponents. then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2 , x ≠ 0, y ≠ 0, z ≠ 0.

We want to simplify a given expression by using exponent properties.

We will get:

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The properties that we will use is:

We start with the expression:

Such that x, y, z ≠ 0

We specify this because we can't divide by zero, so these can't be zero.

First, we can use the second property to rewrite:

Now we rewrite it to:

Now we use the first property:

Finally, we use the second property again:

Where in the last step I wrote the x part in the denominator because you wanted only positive exponents.

If you want to learn more, you can read:

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Step-by-step explanation:

We have to simplify the given expression given as

Therefore simplification of the given expression gives