simplify square root^3 500a^4b^6
To simplify the cube root of 500a^4b^6, we can break down the number into its prime factors and simplify the variables:
500 = 2^2 * 5^3
a^4 = a^3 * a
b^6 = b^3 * b^3
Now we can simplify the cube root expression by taking out the cube roots of each prime factor and grouping them together:
∛500a^4b^6 = ∛(2^2 * 5^3 * a^3 * a * b^3 * b^3)
Taking out the cube roots of each factor, we get:
= 2 * 5 * a * b^2 * ∛(a * b^3)
So the simplified expression is:
2 * 5 * a * b^2 * ∛(a * b^3)