Math, asked by rishiprashar256, 1 month ago

Simplify y^(p(q-r)) y^(q(r-p)) y^(r(p-q))​

Answers

Answered by pulakmath007
0

\displaystyle \sf{  {y}^{p(q - r)}   {y}^{q(r - p)} {y}^{r(p - q)}  } = 1

Given :

\displaystyle \sf{  {y}^{p(q - r)}   {y}^{q(r - p)} {y}^{r(p - q)}  }

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

\displaystyle \sf{  {y}^{p(q - r)}   {y}^{q(r - p)} {y}^{r(p - q)}  }

Step 2 of 2 :

Find the value of the expression

\displaystyle \sf{  {y}^{p(q - r)}   {y}^{q(r - p)} {y}^{r(p - q)}  }

\displaystyle \sf{   = {y}^{p(q - r)}  \times   {y}^{q(r - p)}  \times {y}^{r(p - q)}  }

\displaystyle \sf{   = {y}^{pq - pr}  \times   {y}^{qr - pq}  \times {y}^{pr - qr}  }

\displaystyle \sf{   = {y}^{pq - pr +qr - pq  +pr - qr }  }

\displaystyle \sf{   = {y}^{0 }  }

\displaystyle \sf{   =1  }

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