Simplify the expression 6^-1a^-3b^4/5^-2 ab^5 so that it uses postive exponents. only
(7^2 a^2 b^5/ 7^-1 a^4 b^3)-1 Does this mean:
[(7^2 a^2 b^5) / (7^-1 a^4 b^3)]-1, if that is what you mean, then we have:
Simplify the following:
(7^2 a^2 b^5)/((a^4 b^3)/(7))-1
Multiply the numerator of (7^2 a^2 b^5)/((a^4 b^3)/7) by the reciprocal of the denominator. (7^2 a^2 b^5)/((a^4 b^3)/7) = (7^2 a^2 b^5×7)/(a^4 b^3):
(7^2×7 a^2 b^5)/(a^4 b^3)-1
Combine powers. (7^2 a^2 b^5×7)/(a^4 b^3) = 7^2×7 a^(2-4) b^(5-3):
7^2×7 a^2-4 b^5-3-1
2-4 = -2:
7^2×7 a^-2 b^(5-3)-1
5-3 = 2:
(7^2×7 b^2)/a^2-1
7^2 = 49:
(49×7 b^2)/a^2-1
49×7 = 343:
(343 b^2)/a^2-1
Put each term in (343 b^2)/a^2-1 over the common denominator a^2: (343 b^2)/a^2-1 = (343 b^2)/a^2-(a^2)/a^2:
(343 b^2)/a^2-a^2/a^2
(343 b^2)/a^2-a^2/a^2 = (343 b^2-a^2)/a^2:
Answer: | (343 b^2-a^2)/a^2
