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7^5 times 4^5 is equivalent to (7 times 4)^5, which is 28^5. You could either leave your answer in this format or evaluate 28^5: 17210368.
(153^2)^7 is best done using the rule of exponents (x^a)^b = x^(ab). Multiply the exponents 2 and 7 together: (153^2)^7 = 153^(2*7) = 153^14.
(10^5)(4^5) has two factors, both of which have the exponent 5. We can rewrite this expression as (10*4)^5, which equals 40^5. No, this is not equal to 14^5!