Question 167645
{{{sqrt(3*x^6)* sqrt(27*x^13)}}} ***** equation 1 *****
since {{{sqrt(a)*sqrt(b)}}} = {{{sqrt(a*b)}}}, this becomes:
{{{sqrt(3*x^6*27*x^13)}}}
since a*b*c*d = a*c*b*d, this becomes:
{{{sqrt(3*27*x^6*x^13)}}}
since {{{x^a*x^b = x^(a+b)}}}, this becomes:
{{{sqrt(3*27*x^(6+13))}}}
simplifying, this becomes:
{{{sqrt(81*x^19)}}} ***** equation 2 *****
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to prove the answer is correct, let x be any number that can be easily handled by your calculator.
for example:
let x = 3
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equation 1 becomes:
{{{sqrt(3*3^6)* sqrt(27*3^13)}}}
this becomes:
{{{sqrt(3*729)* sqrt(27*4782969)}}}
this becomes:
{{{sqrt(2187)* sqrt(43046721)}}}
this becomes:
306827.6044.
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equation 2 becomes:
{{{sqrt(81*x^19)}}}
this becomes:
{{{sqrt(81*3^19)}}}
this becomes:
{{{sqrt(81*1162261467)}}}
this becomes:
{{{sqrt(9.414317883*10^10)}}}
this becomes:
306827.6044
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the answers come out the same so equation 1 is equivalent to equation 2.