Determine the value : (3x^5)^_ = 27x^15

3 would be the answer to the blank.

Laws of exponents (indices) say that an exponent raised to another power is simplified by multiplying the exponents
(x^a)^b = x ^ (ab)
and
(xy)^a = (x^a)(y^a)

So let your blank be called a

Using these rules
(3^a)(x^5a) = 27x^15

so 5a = 15, a = 3
check that 3^a = 27 (Yes!)

Solved :-)

the answer would probably be 3 resulting from the solution below:
(3x^5)^_=(27x^15)
=({3^3}x^15)
take out 3 as a common factor:
=(3x^5)^3
(3x^5)^_=(3x^5)^3
so,_=3
hope you understood!

(3x^5)^_ = 27x^15
= (3 x*45)
=(3x^5)^3

blank for power =3

(3x^5)^_ = 27x^15
(3x^5)^_ = 3^3x^(5 × 3)
= (3x^5)^3 = 27x^15
----

I am not sure but the answer from my side would be 3.