Question

class-8,MATHS-EXPONENT AND POWER
solve using laws of exponents
$\frac{({{x}^{m + n}} )^{2} \times ( { {x}^{n + p} })^{2} \times ({ {x}^{p + m} })^{2}}{ {({{x}^{m} } \times {x}^{n} \times {x}^{p}})^{3} }$
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Answer 1

Answer:

The required solution is $x^{m+n+p}$

Step-by-step explanation:

We know that $x^{m}.x^{n}$ = $x^{m+n}$ and $(x^{m})^{n}$ = $x^{mn}$

Using these laws, solving the given problem.

$(x^{m+n})^{2}$ = $x^{2m+2n}$

$(x^{n+p})^{2}$ = $x^{2n+2p}$

$(x^{p+m})^{2}$ = $x^{2p+2m}$

and $(x^{m} * x^{n} * x^{p})^{3}$ = $(x^{m+n+p})^{3}$

The question now becomes,

$\frac{x^{2m+2n}* x^{2n+2p}*x^{2p+2m} }{(x^{m+n+p})^{3}}$

Applying these properties again, we get,

$\frac{x^{2m+2n+2n+2p+2p+2m}}{x^{3m+3n+3p}}$

Solving the exponential powers,

$\frac{x^{4m+4n+4p}}{x^{3m+3n+3p}}$

We also know that $\frac{x^{m} }{x^{n} }$ = $x^{m-n}$

With this property, the term becomes $x^{4m+4n+4p-3m-3n-3p}$

=> $x^{m+n+p}$

which is the required solution.

Answer 2

ANSWER —

${x}^{m + n + p}$

for explanation see the image