Question

Complete the statement using \(>\) or \(<\). $$(5 \cdot 6)^{4} \underline{?} 5 \cdot 6^{4}$$

Short answer

\((5 \cdot 6)^{4} > 5 \cdot 6^{4}\)

Step-by-step solution

Calculate the first expression

In the expression \((5 \cdot 6)^{4}\), the operation within the parentheses should be done first. So, firstly, \(5 \cdot 6\) is calculated which equals \(30\). Now, calculate \((30)^4\) , which equals \(810,000\).

Calculate the second expression

In the expression \(5 \cdot 6^{4}\), according to the order of operation, exponentiation should be done first before multiplication. Therefore, first calculate \(6^{4}\) which equals \(1296\). Then, multiply this result by \(5\), so \(5 \cdot 1296\) equals \(6480\).

Compare the values

Now that both calculations have been made, their results can be compared. \(810,000\) is greater than \(6480\), so the correct symbol to use is \(>\).

Final Statement

Therefore, the complete statement would be \((5 \cdot 6)^{4} > 5 \cdot 6^{4}\).