Question

Simplificando a expressao a×b^-2×( a^-1 x 2)^4 x ( a x b^-1)^2 / ( a^2 b^-1 ) x (a^-1 x b ^2 ) dando o resultado com expoentes positivos

poderiam me mandar com a conta por favor

Answer 1

$a\cdot b^2\cdot \left(\:a^{-1}\cdot 2\right)^4\cdot \frac{\left(\:a\:\cdot \:b^{-1}\right)^2}{\left(\:a^2\:b^{-1}\:\right)}\:\cdot \left(a^{-1}\cdot \:b\:^2\:\right)$$=\left(a\cdot b^2\right)\cdot \left(a^{-1}\cdot \:\:b\:^2\:\right)\cdot \left(\:a^{-1}\cdot 2\right)^4\cdot \frac{\left(\:a\:\cdot \:b^{-1}\right)^2}{\left(\:a^2\:b^{-1}\:\right)}\:$$=b^4\left(\:a^{-1}\cdot 2\right)^4\cdot \frac{\left(\:a\:\cdot \:b^{-1}\right)^2}{\left(\:a^2\:b^{-1}\:\right)}\:$$=\frac{16b^4}{a^4}\cdot \frac{\left(\:a\:\cdot \:b^{-1}\right)^2}{\left(\:a^2\:b^{-1}\:\right)}\:$$=\frac{16b^4}{a^4}\cdot \frac{1}{b}$=$\frac{16b^3}{a^4}$