Question

[(3/7^4x3/7^5)]divided by (3/7)^7

Answer 1

$\frac{1}{11907}$ = ($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)÷($\frac{3}{7}$)⁷

Step-by-step explanation:

Given:

($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)÷($\frac{3}{7}$)⁷

To find:

Simplify the term

Solution:

• We have to simplify the terms. We thus simplify the fractional power term into a simple fractional number.
• The product of power term (aˣ)(aᵇ)=aˣ⁺ᵇ is given by aˣ⁺ᵇ
• On dividing (1÷y) we get  $\frac{1}{y}$=$y^{-1}$, the inverse of y.  

⇒($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)÷($\frac{3}{7}$)⁷

⇒($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)

               

      ($\frac{3}{7}$)⁷

The whole power can be split as ($\frac{3}{7}$)⁷=$\frac{3^{7} }{7^{7} }$. Applying this we get,

⇒($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)

                   

      $\frac{3^{7} }{7^{7} }$

$\frac{1}{y}$=$y^{-1}$ which is the inverse of term y when dividing the term, On applying this format  $\frac{3^{7} }{7^{7} }$ can be $\frac{7^{7} }{3^{7} }$.

⇒($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)×$\frac{7^{7} }{3^{7} }$

Applying the formula (aˣ)(aᵇ)=aˣ⁺ᵇ

⇒3²  ×  7⁷

  7⁷7²    3⁷

On splitting the power terms we get 3⁷=3²3⁵ and 7⁹=7⁷7²

Canceling the like terms we get,

   1      

 7²×3⁵

7²=49 and  3⁵=243 on applying this we get,

⇒   1        

     49×243

⇒ $\frac{1}{11907}$

Thus we get the simple fractional number from the power of the fractional number.

⇒ $\frac{1}{11907}$

Hence,

On simplification we get,

 ($\frac{3}{7^{4} }$×$\frac{3}{7^{5} }$)÷($\frac{3}{7}$)⁷ =   $\frac{1}{11907}$