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

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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

$+- 2$

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

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