Question

.1√a^6 if a<0

Answer 1

Answer:

The answer for first one is,

a³

Answer for Second one is,

n.

Answer for 3rd one is.

-3y

Answer for number four.

x⁹

sorry couldn't answer number 5.

Answer 2

Answer:

To quickly run through them:

1) a³

2) n

3) -3y

4) x⁹

5) 6x

Step-by-step explanation:

An easy way to deal with these is to remember that a square root is just another exponent.  Saying √x is identical to saying $x^{0.5}$.

With that in mind, we can rewrite these expressions.  Take the first question for instance:

$\sqrt{a^6}$

is equivalent to:

$(a^6)^{0.5}$

You may recall that when a number is raised to an exponent, and again raised to an exponent, then those exponents can be multiplied.  6 × 0.5 is equal to 3, which gives us the answer to the first problem:

$(a^6)^{0.5}\\= a^{6 \times 0.5}\\= a^3$

So let's run through the rest of the questions:

$\sqrt{n^2}\\= (n^2)^{0.5}\\= n^{2 \times 0.5}\\= n^1\\= n$

$-\sqrt{9y^2}\\= - 3y^{2 \times 1/2}\\= -3y^1\\= -3y$

$\sqrt{x^{18}} \\= x^{0.5 \times 18}\\= x^9$

$\sqrt{36x^2} \\= 6x^{2 \times 0.5}\\= 6x^1\\= 6x$

In each case, because they're raised to an even power, that eliminates the negativity of the number, so we don't need to worry about complex numbers as the answers.  I'm not sure why the range of the number is specified there if all you need is the question simplified, but hopefully this will explain the answers sufficiently.