Question

2pm thu jan 15 my ixl r.11 simplify exponential expressions using exponent rule simplify. express your answer using exponents. \\(\left(b^{9}c^{4}d^{9}\
ight)^{4}\\)

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So for \((b^{9}c^{4}d^{9})^{4}\), we can apply this rule to each factor inside the parentheses.
\((b^{9}c^{4}d^{9})^{4}=(b^{9})^{4}(c^{4})^{4}(d^{9})^{4}\)

Step2: Apply power of a power rule

The power of a power rule states that \((x^m)^n = x^{m\times n}\). Now we apply this rule to each term:
For \((b^{9})^{4}\), we have \(9\times4 = 36\), so \((b^{9})^{4}=b^{36}\).
For \((c^{4})^{4}\), we have \(4\times4 = 16\), so \((c^{4})^{4}=c^{16}\).
For \((d^{9})^{4}\), we have \(9\times4 = 36\), so \((d^{9})^{4}=d^{36}\).

Step3: Combine the terms

Now we combine the simplified terms together:
\((b^{9})^{4}(c^{4})^{4}(d^{9})^{4}=b^{36}c^{16}d^{36}\)

Answer:

\(b^{36}c^{16}d^{36}\)