Question

which of the following expressions has the greatest value?
$5^2$
$2^5$
$1^{10}$
$3^3$

Explanation:

Step1: Calculate \(5^2\)

\(5^2 = 5\times5 = 25\)

Step2: Calculate \(2^5\)

\(2^5 = 2\times2\times2\times2\times2 = 32\)

Step3: Calculate \(1^{10}\)

\(1^{10}=1\) (since any power of 1 is 1)

Step4: Calculate \(3^3\)

\(3^3 = 3\times3\times3 = 27\)

Step5: Compare the values

We have \(25\) (from \(5^2\)), \(32\) (from \(2^5\)), \(1\) (from \(1^{10}\)), and \(27\) (from \(3^3\)). Comparing these values: \(1<25<27<32\)

Answer:

\(2^5\)