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

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Answer 1 · 2017-10-26T15:49:33

$t^{53} u^{21} v^{6}$ $t^53u^21v^6$

$t^{8} u^{19} v^{6} t^{37} u v^{0} t^{8} u v^{0}$ $t^8u^19v^6t^37uv^0t^8uv^0$

laws of indices:

$a^{m} \cdot a \cdot n = a^{m + n}$ $a^m*a*n=a^(m+n)$
$a^{0} = 1$ $a^0=1$

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

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

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

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

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

How do you solve t^ { 8} u ^ { 19} v ^ { 6} \cdot t ^ { 37} u v ^ { 0} \cdot t ^ { 8} u v ^ { 0}t8u19v6⋅t37uv0⋅t8uv0t^ { 8} u ^ { 19} v ^ { 6} \cdot t ^ { 37} u v ^ { 0} \cdot t ^ { 8} u v ^ { 0}?