How do I simplify and evaluate exponential expressions?

Question

For example,

(4x)^2

(5x^2)^4

(-3a^2c)(3b^3c^7)4

-(a^7b^2)^4 • (-a^4b^9)^2

How would I solve these?
And what are the laws I follow?

Answer 1

(a*b)^c = (a^b)*(b^c)
(a^b)^c = a^(b*c)
(a^b)(a^c)=a^(b+c)

(4x)^2 = 16 x^2
(5x^2)^4 = 625 x^8
(-3a^2c)(3b^3c^7)^4=-3a^2c3^4b^12c^28=243a^2b^12c^31
-(a^7b^2)^4 • (-a^4b^9)^2=a^28b^8a^8b^18=a^36b^26

Answer 2

In a product raise each factor to the exponent (4x)^2=16x^2
To raise a exponent to an exponent multiply both exponents
(5x^2)^4 = 5^4*x^8 = 625 x^8
To multpy exponential of the same base sum the exponents
-3^5a^2b^12c^29-a^36b^26