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:

$9^6=531441$