How do you simplify #2^sqrt7*2^sqrt7#?

Question

1757 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-10T20:15:02

Simplified, the expression is #4^sqrt7#.

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 actual problem:

# color(white)=2^color(red)sqrt7*2^color(blue)sqrt7 #

# =2^(color(red)sqrt7+color(blue)sqrt7) #

# =2^(color(purple)(2sqrt7)) #

# =2^(2*color(purple)sqrt7) #

# =(2^2)^color(purple)sqrt7 #

# =4^color(purple)sqrt7 ~~ 39.16525... #

That's as simplified as it gets, unfortunately.

Answer 2 · 2018-03-10T20:15:32

#4^7= 16384#

#2^sqrt7*2^sqrt7#
#2*2=4#
#1^sqrt7*1^sqrt7= 1^7 #
#4*1^7= 4^7#
#4*4*4*4*4*4*4= 4^7= 16384#