Question

1. evaluate \\(\frac{-5x^3y^5}{15x^{-7}y^5z^3}\\) for x = -1, y = 5, and z = 3

Explanation:

Step1: Simplify the coefficient

$\frac{-5}{15} = -\frac{1}{3}$

Step2: Simplify $x$-terms using exponent rules

$x^{3 - (-7)} = x^{10}$

Step3: Simplify $y$-terms using exponent rules

$y^{5 - 5} = y^0 = 1$

Step4: Combine simplified terms

$-\frac{1}{3}x^{10}z^{-3} = -\frac{x^{10}}{3z^3}$

Step5: Substitute $x=-1, z=3$

$-\frac{(-1)^{10}}{3\times3^3}$

Step6: Calculate numerator and denominator

$(-1)^{10}=1$, $3\times3^3=3^4=81$

Step7: Compute final value

$-\frac{1}{81}$

Answer:

$-\frac{1}{81}$