Question

(216^7)^3:(36^5)^4=?

Answer 1

216^21:36^20=216^21/36^20=(6^3)^21/(6^2)^20=6^63/6^40=6^23

Answer 2

To simplify the expression (216^7)^3:(36^5)^4, we can first calculate the exponents and then divide the results.

Let's start by simplifying the exponents:

(216^7)^3 = 216^(73) = 216^21 (36^5)^4 = 36^(54) = 36^20

Now, we can perform the division:

(216^7)^3:(36^5)^4 = 216^21 / 36^20

To make the division easier, we can express 216 and 36 as powers of 6:

216 = 6^3 36 = 6^2

Now, the expression becomes:

(6^3)^21 / (6^2)^20

Using the rule (a^m)^n = a^(m*n), we can simplify further:

6^(321) / 6^(220) = 6^63 / 6^40

Now, when you divide two numbers with the same base (in this case, both are 6), you can subtract the exponents:

6^(63-40) = 6^23

So, the simplified expression is 6^23.