Question

Find the multiplicative inverse of 3 ^-3 *

Answer 1

Step-by-step explanation:

The multiplicative inverse of 3 ^-3 is 3^3 (or) 27

Answer 2

The multiplicative inverse of $\sf {3}^{ - 3}$ is 27

Given :

The number $\sf {3}^{ - 3}$

To find :

The multiplicative inverse

Solution :

Step 1 of 2 :

Define multiplicative inverse of a number

1 is the Multiplicative identity

Let M ( ≠ 0 ) is the multiplicative inverse of N

Then M × N = 1 = N × M

⇒ M = 1/N

So 1/N is multiplicative inverse of N

Step 2 of 2 :

Find multiplicative inverse of $\sf {3}^{ - 3}$

Let N be the multiplicative inverse of $\sf {3}^{ - 3}$

Then we have ,

$\displaystyle \sf{N \times {3}^{ - 3} = 1}$

$\displaystyle \sf{ \implies N \times \frac{1}{ {3}^{3} } = 1}$

$\displaystyle \sf{ \implies N \times \frac{1}{ 27} = 1}$

$\displaystyle \sf{ \implies N = 27}$

The multiplicative inverse of $\sf {3}^{ - 3}$ is 27

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