Question

Solve the equation and keep it in exponent-based form.

Answer 1

Explanation:

Anything raised to zero = 1

`a^(0) = 1\\\\a^(m)*a^(n) =a^(m+n)\\\\(a^(m))/(a^(n))=a^(m- n)\\`

In exponent multiplication, if base are same, just add the powers.

In exponent division, if bases are same, subtract the powers.

`(a^(m))^(n) =a^(m*n)`

`(3^(-2)* 4^(-5)*5^(0))^(-3) * \left((4^(-4))/(3^(3)) \right)^(3)*3^(3) \\\\\\= (3^(-2)* 4^(-5)*1)^(-3) * \left((4^(-4))/(3^(3)) \right)^(3)*3^(3)\\\\\\= 3^(-2*(-3)) *4^(-5*(-3)) * (4^(-4*3))/(3^(3*3))*3^(3)\\\\\\=3^(6)*4^(15)*(4^(-12))/(3^(9))*3^(3)\\\\\\= 3^(6+3-9)* 4^(15+(-12))\\\\=3^(0)*4^(3)\\\\=1*4^(3)\\\\=4^(3)`