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denis23 [38]
3 years ago
7

What is the product of a,b, and c?

Mathematics
1 answer:
Yuri [45]3 years ago
6 0

Answer:

abc =  -  \frac{16}{3}

Step-by-step explanation:

{x}^{ - 2}  {y}^{3}  \sqrt[3]{ 64{x}^{5}  {y}^{3} }  = a {x}^{b}  {y}^{c}  \\  \\  {x}^{ - 2}  {y}^{3}   \times 4 \times  {x}^{ \frac{5}{3} }   \times y= a {x}^{b}  {y}^{c}   \\  \\ 4 {x}^{ \frac{5}{3} - 2 }  {y}^{3 + 1}  = a {x}^{b}  {y}^{c}   \\  \\ 4 {x}^{ \frac{5 - 6}{3} }  {y}^{4}  = a {x}^{b}  {y}^{c}   \\  \\ 4 {x}^{ \frac{ - 1}{3} }  {y}^{4}  = a {x}^{b}  {y}^{c}   \\  \\ equating \: like \: terms \: on \: both \: sides \\  \\ a = 4 \\  \\ b =   - \frac{1}{3}  \\  \\ c = 4 \\  \\ abc = 4 \times ( -  \frac{1}{3} ) \times 4 \\  \\  = 16 \times ( -  \frac{1}{3} ) \\  \\ abc =  -  \frac{16}{3}

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