Question

Complete the statement using \(>\) or \(<\). $$ \left(7^{2}\right)^{3} \geq 7^{5} $$

Short answer

Based on the solution steps, \((7^{2})^{3}\) is greater than \(7^{5}\), so the completed statement is \((7^{2})^{3} > 7^{5}\).

Step-by-step solution

Simplify the first expression

Begin by simplifying the first expression. An exponential expression can be simplified by multiplying the exponents, so \((7^{2})^{3}\) simplifies to \(7^{2*3}\) which is equal to \(7^{6}\).

Compare the expressions

Now that we have simplified the first expression to \(7^{6}\), we can compare this to the second expression, \(7^{5}\). Since \(7^{6}\) as the base 7 is being raised to a higher power than \(7^{5}\), it is clear that \(7^{6} > 7^{5}\).