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Gekata [30.6K]
3 years ago
5

I'll mark brainliest just tell me how to.

Mathematics
1 answer:
IRINA_888 [86]3 years ago
3 0

Answer:

a = 12

b = 2

c = 11

Step-by-step explanation:

\frac{( {x}^{5}y  {z}^{4} )^{3} }{ {x}^{3} yz}  =  {x}^{a}  {y}^{b}  {z}^{c}  \\  \\ \frac{ {x}^{5 \times 3}y^{3}   {z}^{4 \times 3} }{ {x}^{3} yz}  =  {x}^{a}  {y}^{b}  {z}^{c}  \\  \\ \frac{ {x}^{15}y^{3}   {z}^{12} }{ {x}^{3} yz}  =  {x}^{a}  {y}^{b}  {z}^{c}  \\  \\  {x}^{15 - 3}  {y}^{3 - 1}  {z}^{12 - 1} =  {x}^{a}  {y}^{b}  {z}^{c} \\  \\  {x}^{12}  {y}^{2}  {z}^{11} =  {x}^{a}  {y}^{b}  {z}^{c}  \\  \\ equating \: like \: terms \: from \: both \: sides \\  \\  {x}^{12}  =  {x}^{a}  \:  \implies \: a = \boxed{ 12}\\  \\  {y}^{2}  =  {y}^{b}  \:  \implies \: b = \boxed{ 2} \\  \\  {z}^{11}  =  {z}^{c}  \:  \implies \: c = \boxed{ 11}

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