Question

9^2*9^3=59,049Using only this information and the laws of exponents, explain how youcouldcompute"

Answer 1

a) We want to calculate:

`9^6`

We can write the last equation in the following form:

`9^(1+5)=9^1\cdot9^5=9\cdot(9^5)=9\cdot(9^2\cdot9^3)`

Where we have used the laws of exponents. Now we can replace the terms inside the parenthesis with the equation of the statement and find that:

`9\cdot(9^2\cdot9^3)=9\cdot59049=531441`

Where in the last step we just multiplied 9 with 59049.

b) We consider:

`(81)^3=531441`

We know that: 81 = 9*9 = 9^2 , so using that, and the laws of exponents we conclude that:

`(81)^3=(9\cdot9)^3=(9^2)^3=9^(2\cdot3)=9^6^{}^{}`

So:

`9^6=531441`