Question

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Simplify and express as a power of rational number with positive exponents......
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Class 8​

Answer 1

Question :-

Simplify and express as a power of rational number with positive exponents :-

$\sf { \dfrac{51}{19} }^{ - 3} \times { \dfrac{51}{19} }^{ - 2} \times { \dfrac{51}{19} }^{ - 4}$

Concept :-

The laws of exponent used -

$\sf a^m \times a^n = a^{(m + n)}$

$\sf a^{-n} = \dfrac{1}{a^n}$

Solution :-

$\sf { \dfrac{51}{19} }^{ - 3} \times { \dfrac{51}{19} }^{ - 2} \times { \dfrac{51}{19} }^{ - 4}$

$\sf = { \dfrac{51}{19} }^{(-3) + ( -2) + (-4)}$

$\sf = \dfrac{51}{19} ^{ -3 -2-4}$

$\sf = \dfrac{51}{19}^{-9}$

According to the question, the rational should have positive power -

$\sf \dfrac{51}{19}^{-9} = \dfrac{19}{51}^{9}$

$\boxed{\sf { \dfrac{51}{19} }^{ - 3} \times { \dfrac{51}{19} }^{ - 2} \times { \dfrac{51}{19} }^{ - 4} = \dfrac{19}{51}^{9}}$

Answer 2

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Step-by-step explanation:

Question :-

Simplify and express as a power of rational number with positive exponents :-

51

−3

×

19

51

−2

×

19

51

−4

Concept :-

The laws of exponent used -

\sf a^m \times a^n = a^{(m + n)}a

m

×a

n

=a

(m+n)

\sf a^{-n} = \dfrac{1}{a^n}a

−n

=

a

n

1

Solution :-

\sf { \dfrac{51}{19} }^{ - 3} \times { \dfrac{51}{19} }^{ - 2} \times { \dfrac{51}{19} }^{ - 4}

19

51

−3

×

19

51

−2

×

19

51

−4

\sf = { \dfrac{51}{19} }^{(-3) + ( -2) + (-4)}=

19

51

(−3)+(−2)+(−4)

\sf = \dfrac{51}{19} ^{ -3 -2-4}=

19

51

−3−2−4

\sf = \dfrac{51}{19}^{-9}=

19

51

−9