Algebraic Theory

1. Do the operations and simplify.

(a^-2b^3)/(x^-8y) . (a^6b^2)/(x^8y^4)


2. Do the operations and simplify.

(x^2 + 8x + 16)/(x) . (x^2 - 4x)/(x^2 - 16)


3. Do the operations and simplify.

(a + 5)/(25 - a^2) . (5a - 25)/(5a + 25)


4. Simplify the expression.

(x2 - 36)/(x^2 - 64) ÷ (x + 6)/(x - 8)


5. Simplify the cube root.

^3√[8a^30b^21]


6. Simplify and combine like radicals  . All variables represent positive numbers.

8^5√[3y] - 2^5√[3y]



7. Simplify and combine like radicals.

  √[45] - √[245]


8. Multiply  and simplify the result.

   √[125b]  and √[5b^3n]



9. Multiply and simplify the result.

  3√[2](9√[6] + 3√[5])



10. Simplify the expression by rationalizing the denominator.

   √[3/7]