Questions: Simplify. [ (-8 x^2 z^4)^2 ] Write your answer without parentheses.

Solution Steps

To simplify the given expression, we need to apply the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\). We will apply this rule to each term inside the parentheses.

We start with the expression \(\left(-8 x^{2} z^{4}\right)^{2}\). To simplify this, we apply the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\). This means we will raise each component inside the parentheses to the power of 2.

• For the coefficient: \[ (-8)^{2} = 64 \]
• For \(x^{2}\): \[ (x^{2})^{2} = x^{2 \cdot 2} = x^{4} \]
• For \(z^{4}\): \[ (z^{4})^{2} = z^{4 \cdot 2} = z^{8} \]

Combining all the simplified components, we get: \[ 64 x^{4} z^{8} \]

Final Answer