Question

which expression is equivalent to $7^5 \cdot 9^5$?
$63^{25}$ $\frac{1}{63^5}$
$63 \cdot 63^4$ $63^{10}$

Explanation:

Step1: Recall the exponent rule for products

The rule \(a^n \cdot b^n=(a \cdot b)^n\) applies here. For \(7^5 \cdot 9^5\), we can rewrite it as \((7\times9)^5\).

Step2: Calculate \(7\times9\)

\(7\times9 = 63\), so \(7^5 \cdot 9^5=(7\times9)^5 = 63^5\).

Step3: Simplify \(63\cdot63^4\)

Using the rule \(a^m\cdot a^n=a^{m + n}\), for \(63\cdot63^4\), we have \(63^1\cdot63^4=63^{1 + 4}=63^5\), which matches the result from Step 2.

Answer:

\(63\cdot63^4\)