Question

Which expression is equivalent to the expression shown?

(59)°: 5"
5
51
15
5
To
524

Answer 1

`5^(15)`

Given:

`(5^3)^9/5^(12)`

Let us first apply the Power Rule which states that:

`(a^x)^y=a^(xy)`

With this, we now know that:

`(5^3)^9=5^(3*9)=5^(27)`

Our expression now becomes:

`5^(27)/5^(12)`

Now, applying the Quotient Rule which states that:

`a^x/ a^y=a^(x-y)`

We can evaluate the given expression as:

`5^(27)/5^(12)=5^(27-12)^{}`

And this will give us a result of

`5^(15)`