How do you simplify #(2ag^2)^4(3a^2g^3)^2#?

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Answer 1 · 2018-06-15T04:47:53

#144a^8g^14#

#(2ag^2)^4(3a^2g^3)^2#

First, let's look at #(2ag^2)^4#. The exponent #4# applies to everything inside the parenthesis, so:
#2^4 = 16#

#a^4 = a^4#

#(g^2)^4 = g^(2*4) = g^8#

Multiply them all together:
#16a^4g^8#

Now #(3a^2g^3)^2#:
#3^2 = 9#

#(a^2)^2 = a^(2*2) = a^4#

#(g^3)^2 = g^(3*2) = g^6#

Multiply them all together:
#9a^4g^6#

Now multiply both simplified expressions:
#(16a^4g^8)(9a^4g^6)#

Simplify:
#144a^(4+4)g^(8+6)#

Therefore, the simplified expression is:
#144a^8g^14#

Hope this helps!