Question

by what number should
$( \frac{ - 5}{11} )^{ - 3}$
be multiplied with to get
$( \frac{ - 11}{5} )^{6}$


please solve it​

Answer 1

Step-by-step explanation:

Given:-

(-5/11)^-3

To find:-

By what number should (5/11)^-3 be multiplied with to get (-11/5)^6.

Solution:-

Given number is (-5/11)^-3

Let the required number be X

(-5/11)^-3 should be multiplied with X to get (-11/5)^6

=> (-5/11)^-3 × X = (-11/5)^6

We know that

a^-n = 1/a^n

=>1/(-5/11)^3 × X = (-11/5)^6

=>X=(-11/5)^6×(-5/11)^3

We know that

(ab)^m = a^m×b^n

=>X = [(-11)^6/5^6] × [(-5)^3/(11^3)]

=>X=[(-11)^6/(11^3)] ×[(-5)^3/5^6]

=>X=[(11)^6/(11^3)] ×[(-5)^3/5^6]

We know that

a^m/a^n = a^(m-n)

=>X=(11)^(6-3) × (-(5^(3-6))

=>X=11^3 × -(5^-3)

=>X=11^3× -1/5^3

EWe know that

(a/b)^m = a^m/a b^n

=>X=(-11/5)^3

X = (-11/5)^3

Answer:-

The required number = (-11/5)^3

Used formulae:-

• a^-n = 1/a^n
• a^m/a^n = a^(m-n)
• (ab)^m = a^m×b^n
• (a/b)^m = a^m/a b^n

Answer 2

Answer:

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