Question

By what number should 3power-4 multiplied so that product is 729

Answer 1

Answer:

The number is $\sf{(3)^{10}.}$

Step-by-step explanation:

Let the number be N.

A.T.Q.

Equation formed will be :

→ ${\sf{ {(3)}^{-4}}}$ × N = 729

• ${\boxed{\tt{\red{Identity : a^{- n} = {\dfrac{1}{a^n}} }}}}$

→ ${\sf{ {\dfrac{1}{ {(3)}^{4} }}}}$ × N = 729

Transposing the terms, we get

→ N = 729 × ${\sf{ (3)^{4} }}$

We can write 729 as a multiple of 3.

→ N = ${\sf{ (3)^6 × (3)^4}}$

• ${\boxed{\tt{\red{Identity : a^m × a^n = a^{m + n} }}}}$

→ N = $\sf{ (3)^{6 + 4} }$

→ N = ${\sf{ (3)^{10} }}$