How do you simplify #2^(1/4) * 8^(1/4)#?

Question

3429 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T00:31:04

The simplified expression is #2#.

Use these exponent rules to simplify the expression:

#x^color(red)m+x^color(blue)n=x^(color(red)m+color(blue)n)#

#(x^color(red)m)^color(blue)n=x^(color(red)m*color(blue)n)#

Now here's the expression. Rewrite #8# as #2^3#, then use the exponent rules to simplify:

#color(white)=2^(1/4)*8^(1/4)#

#=2^color(green)(1/4)*(2^color(red)3)^color(blue)(1/4)#

#=2^color(green)(1/4)*2^(color(red)3*color(blue)(1/4))#

#=2^color(green)(1/4)*2^(color(blue)(color(red)3/4)#

#=2^(color(green)(1/4)+color(blue)(color(red)3/4))#

#=2^(color(blue)((color(green)1color(black)+color(red)3)/4))#

#=2^(color(blue)(color(brown)4/4)#

#=2^1#

#=2#

Answer 2 · 2018-03-11T00:32:23

#+- 2#

#2^(1/4) * 8^(1/4)#
#color(white)("XXX")=(2 * 8)^(1/4)#
#color(white)("XXX")=16^(1/4)#
#color(white)("XXX")=+-root(4)(16)#
#color(white)("XXX")=+-2#