Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

Question

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.  16u^3v/uv^7

Answer 1

Simplify under the radical (square root sign) first

the square root of (16u³v/uv⁷)

u³ / u when you are dividing the same bases, subtract the exponents

u³/u = u²/1

v/v⁷ = 1/v⁶

This gives us the square root of 16u²/v⁶

Take the square root of each factor-

the square root of 16 is 4

the square root of u² is u

the square root of 1/v⁶ is 1/v³

The answer is 4u/v³

Answer 2

4u/v^3 is the square root of 16u^3v/uv^7

u^3/u = u^2

v/v^7=v^-6 = 1/v^6

square root of 16 =4

square root of u^2 =u^1=u to take a square root of a power, just divide the power in half 2/2=1

square root of 1/v^6=1/v^3 take half of 6 to get 3

multiply those 3 roots to get 4u/v^3