Simplify the expression. Write the result using positive exponents only.
(-2x^3y^-4)(5x^-1y)
(-2x^3y^-4)(5x^-1y)
= (-2)(5)(x^3)(x^-1)(y^-4)(y^-4)(y)
= -10 x^2 y^-3
or
= -10x^2/y^3
To simplify the expression (-2x^3y^-4)(5x^-1y), we can apply the rules of exponents.
First, let's multiply the coefficients and combine them:
(-2 * 5) = -10
Next, let's multiply the variables with the same base, x and y, and add their exponents:
x^3 * x^-1 = x^(3 + (-1)) = x^2
y^-4 * y = y^(-4 + 1) = y^-3 = 1/y^3 (remember that when you have a negative exponent, you can rewrite it as the reciprocal of the positive exponent)
Now, let's put it all together:
(-10)(x^2)(1/y^3) = -10x^2/y^3
Therefore, the simplified expression is -10x^2/y^3, written with positive exponents.