Question

Which is greater: 5⁶ or 6⁵?
a) 5⁶
b) 6⁵

Answer 1

a) 5^6

Step-by-step explanation:

With exponents, there is no real easy way to tell except to plug them into a calculator.

5^6 = 15625

6^5 = 7776

One trick I can offer is that numbers with larger exponents tend to be a lot bigger, even if it's just by one like in this problem.

The difference between 12^2 and 12^3 is an easy way of seeing this

12^2 = 144

12^3 = 1728

Answer 2

5⁶ (15,625) is greater than 6⁵ (7,776). Therefore, 5⁶ is the larger value.

Step-by-step explanation:

To determine which is greater between 5⁶ (5 to the sixth power) and 6⁵ (6 to the fifth power), we can calculate the values of each:

• 5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 15,625
• 6⁵ = 6 × 6 × 6 × 6 × 6 = 7,776

Comparing the two results, we see that 15,625 is greater than 7,776, so 5⁶ is greater than 6⁵.