How do you simplify ((5x)/(3yz))^-3(5x3yz)3 and write it using only positive exponents?

1 Answer
Jan 14, 2018

See a solution process below:

Explanation:

First, let's use this rule of exponents to rewrite the expression as:

1/4y + (1/4 xx 3/2) =>14y+(14×32)

((5x)/(3yz))^color(red)(-3) => 1/((5x)/(3yz))^color(red)(- -3) => 1/((5x)/(3yz))^3(5x3yz)31(5x3yz)31(5x3yz)3

Now, use these rules of exponents to eliminate the outer exponent:

a = a^color(red)(1)a=a1 and (x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×b

1/((5^color(red)(1)x^color(red)(1))/(3^color(red)(1)y^color(red)(1)z^color(red)(1)))^color(blue)(3) => 1/((5^(color(red)(1)xxcolor(blue)(3))x^(color(red)(1)xxcolor(blue)(3)))/(3^(color(red)(1)xxcolor(blue)(3))y^(color(red)(1)xxcolor(blue)(3))z^(color(red)(1)xxcolor(blue)(3)))) => 1/((5^3x^3)/(3^3y^3z^3)) => 1/((125x^3)/(27y^3z^3)) => (27y^3z^3)/(125x^3)1(51x131y1z1)3151×3x1×331×3y1×3z1×3153x333y3z31125x327y3z327y3z3125x3