Question

simplify. express your answer using exponents.
$(c^{8}d^{9})^{7}$

Explanation:

Step1: Apply power of a product rule

When raising a product to a power, we raise each factor to that power. So, \((c^{8}d^{9})^{7} = (c^{8})^{7} \cdot (d^{9})^{7}\)

Step2: Apply power of a power rule

The power of a power rule states that \((a^{m})^{n}=a^{m\times n}\). For \((c^{8})^{7}\), we multiply the exponents: \(8\times7 = 56\), so \((c^{8})^{7}=c^{56}\). For \((d^{9})^{7}\), we multiply the exponents: \(9\times7 = 63\), so \((d^{9})^{7}=d^{63}\)

Step3: Combine the results

Putting it back together, we have \(c^{56}d^{63}\)

Answer:

\(c^{56}d^{63}\)