Answer :

GinnyAnswer
Sure, let's simplify the given expression step by step.

We start with the expression:

[tex]\[ \left(\frac{-2 y^2}{z}\right)^5 \][/tex]

First, apply the power of 5 to both the numerator and the denominator inside the parentheses. This is a property of exponents:

[tex]\[ \left(\frac{-2 y^2}{z}\right)^5 = \frac{(-2 y^2)^5}{z^5} \][/tex]

Next, focus on the numerator [tex]\((-2 y^2)^5\)[/tex]. We can distribute the exponent to both [tex]\(-2\)[/tex] and [tex]\(y^2\)[/tex]:

[tex]\[ (-2 y^2)^5 = (-2)^5 \cdot (y^2)^5 \][/tex]

Now, calculate [tex]\((-2)^5\)[/tex]:

[tex]\[ (-2)^5 = -32 \][/tex]

Next, apply the power of 5 to [tex]\(y^2\)[/tex]:

[tex]\[ (y^2)^5 = y^{2 \cdot 5} = y^{10} \][/tex]

Putting these results together, the numerator becomes:

[tex]\[ (-2)^5 \cdot (y^2)^5 = -32 \cdot y^{10} \][/tex]

So our expression now is:

[tex]\[ \frac{-32 \cdot y^{10}}{z^5} \][/tex]

Simplifying this, the final simplified form of the given expression is:

[tex]\[ -32 \cdot \frac{y^{10}}{z^5} \][/tex]

Or simply:

[tex]\[ -32 \cdot y^{10} / z^5 \][/tex]

So, the simplified expression is:

[tex]\[ -32 \cdot y^{10} / z^5 \][/tex]

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