# Simplify this #sqrt(9^(16x^2)) # ?

##### 3 Answers

(assuming you only want the primary square root)

#### Explanation:

Since

#### Explanation:

#### Explanation:

You can simplify this expression using various properties of radicals and exponents. For example, you know that

#color(blue)(sqrt(x) = x^(1/2))" "# and#" "color(blue)((x^a)^b = x^(a * b))#

In this case, you would get

#sqrt(9^(16x^2)) = [9^(16x^2)]^(1/2) = 9^(16x^2 * 1/2) = 9^(8x^2)#

Since you know that

#9^(8x^2) = (3^2)^(8x^2) = 3^(16x^2)#

Another approach you can use is

#sqrt(9^(16x^2)) = sqrt((9^(8x^2))^2) = 9^(8x^2) = 3^(16x^2)#

Alternatively, you can also use

#sqrt(9^(16x^2)) = sqrt((9^(x^2))^16) = (9^(x^2))^8 = [(3^2)^(x^2)]^8 = 3^(16x^2)#