Question

Simplify 4 to the 7th over 5 squared all raised to the 3rd power.

Answer 1

(4^7/5^2)^ 3

= 4^21 / 5^6

which according to my calculator is 281,474,976.7   approximately

Answer 2

Multiply the exponents 

for example, (2^3)^5 = 2^(3*5) = 2^15 
why? 
2^3 = 2*2*2 
(2^3)^5 = 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2 * 2*2*2 

^ is just shorthand for ***... 
Just as * is shorthand for +++... 

2*3*4 = 2+2+2 + 2+2+2 + 2+2+2 + 2+2+2