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

3 Answers
Alan P.
Sep 9, 2015

#sqrt(9^(16x^2)) = 9^(8x^2) = 43,046,721^(x^2)#
(assuming you only want the primary square root)

Explanation:

Since #b^(2m) = (b^m)^2#

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

#color(white)("XXX") = 9^(8x^2)#

#color(white)("XXX") = (9^8)^(x^2)#

#color(white)("XXX")=43,046,721^(x^2)#

Jim H
Sep 9, 2015

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

Explanation:

#sqrt(9^(16x^2)) = (9^(16x^2))^(1/2) = 9^((1/2)16x^2)#

# = (9^(1/2))^(16x^2) = 3^(16x^2)# OR #=9^((1/2*16)x^2) = 9^(8x^2)#

Stefan V.
Sep 9, 2015

#3^(16x^2)#

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 = 3^2#, you can rewrite this as

#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)#

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