How do you solve #t^ { 8} u ^ { 19} v ^ { 6} \cdot t ^ { 37} u v ^ { 0} \cdot t ^ { 8} u v ^ { 0}#?

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Answer 1 · 2017-10-26T15:49:33

#t^53u^21v^6#

#t^8u^19v^6t^37uv^0t^8uv^0#

laws of indices:

#a^m*a*n=a^(m+n)#
#a^0=1#

#t^8u^19v^6t^37uv^0t^8uv^0 = t^8u^19v^6t^37ucancel(v^0)t^8ucancel(v^0)#

#=t^8u^19v^6t^37ut^8u#

#=t^8t^37t^8 * u^19u u * v^6#

#=t^53u^21v^6#

Answer 2 · 2017-10-26T15:56:34

#t^53u^21v^6#

First, we need to know
#a^m * a^n = a^(m+n)#

#(a^m) / (a^n) = a^(m-n)#
( additional info. , in this question, we won't use it )

#a^0 =1#

#a=a^1#

Then, to do this question, we can first group the like term together:

#t^8u^19v^6*t^37uv^0*t^8uv^0#
#=(t^8*t^37*t^8)(u^19*u^1*u^1)(v^6*v^0*v^0)#
#=(t^(8+37+8))(u^(19+1+1))(v^6*1*1)#
#=t^53u^21v^6#

this is the answer :) Hope it can help you