Question

If m=3 and n=2 find the value of
$9m { }^{2} - 10n {}^{3}$
$2m {}^{2} n {}^{2}$
$2m {}^{3} + 3n {}^{2} - 5m {}^{2}n$
$m {}^{n} - n {}^{m}$


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Answer 1

Given :-

• m=3 and n=2

To find :-

1. $9m { }^{2} - 10n {}^{3}$
2. $2m {}^{2} n {}^{2}$
3. $2m {}^{3} + 3n {}^{2} - 5m {}^{2}n$
4. $m {}^{n} - n {}^{m}$

Solution :-

• m = 3 and n = 2

${\bf{\red{1)9m { }^{2} - 10n {}^{3}}}}$

$\implies\sf 9\times{3}^{2} - 10\times{2}^{3}$

$\implies\sf 9\times{9} - 10\times{8}$

$\implies\sf 81 - 80=1$

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${\bf{\red{2)2m {}^{2} n {}^{2}}}}$

$\implies\sf 2\times{3}^{2}\times{2}^{2}$

$\implies\sf 2\times{9}\times{4}$

$\implies\sf 18\times{4}=72$

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${\bf{\red{3)2m {}^{3} + 3n {}^{2} - 5m {}^{2}n}}}$

$\implies\sf 2\times{3}^{3} + 3\times{2}^{2} - 5\times{3}^{2}\times{2}$

$\implies\sf 2\times{27} + 3\times{4}- 5\times{9}\times{2}$

$\implies\sf 54+ 12- 90$

$\implies\sf -24$

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${\bf{\red{4)m {}^{n} - n {}^{m}}}}$

$\implies\sf 3 {}^{2} - 2 {}^{3}$

$\implies\sf 9 - 8=1$

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Answer 2

Step-by-step explanation:

Given : -

• If m=3 and n=2.

Solution :) ( 1 )

If m = 3 and n = 2 ,

Value of 9m² - 10n³

= 9 × 3² - 10 × 2³

= 9 × 9 - 10 × 8

= 81 - 80

= 1

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Solution :) ( 2 )

= 2m²n²

= 2(3)²(2)²

= 2 ×9 ×4

= 72

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Solution :) ( 3 )

2m³+ 3n² – 5m²n

= 2(3)³ + 3(2)² – 5(3)²(2)

= 2(27) + 3(4) – 5(9)(2)

= 54 + 12 – 90

= - 24

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Solution :) ( 4 )

(m^n) - (n^m)

= 3²- 2³

= 9 - 8

= 1

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