Question

simplify. express your answer using exponents.
$(x^{9}y^{9}z^{-6})^{7}$

Explanation:

Step1: Apply Power of a Product Rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((x^{9}y^{9}z^{-6})^{7}\), we can apply this rule to each factor:
\(x^{9\times7}y^{9\times7}z^{-6\times7}\)

Step2: Calculate the Exponents

Calculate each exponent:

• For \(x\): \(9\times7 = 63\), so \(x^{63}\)
• For \(y\): \(9\times7 = 63\), so \(y^{63}\)
• For \(z\): \(-6\times7=-42\), so \(z^{-42}\)

Combining these, we get \(x^{63}y^{63}z^{-42}\)

Answer:

\(x^{63}y^{63}z^{-42}\)