Question

which expressions are equivalent to √25d · d 1/3 ?

Answer 1

@SmokeyBrown

Answer 2

So, when multiplying variables with exponents, we add the exponents. We can simplify the expression as 5d^1/2 * d^1/3
So, to get the proper exponent for the product, we add 1/2 to 1/3. This is the same as 3/6 plus 2/6, or 5/6.
So, just the first option ad the last option would be correct.

Answer 3

I must be getting tired, haha

Answer 4

i don't blame you lol

Answer 5

4 last questions and that's it

Answer 6

Ok, we can start by taking 4sqrt(9^15) and converting it to 9^15/4. Likewise, we can convert sqrt(3^3) to 3^3/2. Now, 9 and 3 aren't the same term, so we can either convert 9^15/4 to 3^15/2 or we can convert 3^3/2 to 9^3/4
When we multiply our two terms, we get either 9^18/4, or 3^18/2. Note that these two values are equivalent.
Now, we can take this to the power of 2/27. In that case, we multiply exponents.
Our result would be 9^36/108 or 3^36/54.
Now, the latter result can be simplified to 3^2/3, so that would be our answer.