How do you solve #(2x+7)^(3/2)=27#?

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Answer 1 · 2016-03-19T15:32:05

We must first convert to radical form by using the exponent rule #a^(m/n) = root(n)(a^m)#

#sqrt((2x + 7)^3) = 27#

We can get rid of the radical by squaring both sides of the equation.

#(2x + 7)^3 = 729#

Now, to cancel the cube, we must take the cube root of #729#.

#2x + 7 = 9#

#2x = 2#

#x = 2/2#

#x = 1#

Practice exercises:

Solve for x:

a). #(2x + 1)^(3/2)= 7x - 1#

b). #8^(x/3) = 3x + 4#

Good luck!