Question 1175448
see my worksheet shown below:


<img src = "http://theo.x10hosting.com/2021/022004.jpg" >


step 1 shows the problem, which is Q * P / R.


the base is 3m + 5 which is the same in Q and P and R.


step 2 uses the exponent arithmetic property that says that b^x * b^y = b^(x + y).


step 3 uses the exponent arithmetic property that says that b^x / b^y = b^(x - y).


step 4 provides the results of the exponent arithment properties being applied to the problem.


step 5 shows the final results.


i checked with my calculator by applying random values to m and a and b and then evaluating the initial equation and the final equation to confirm that they would provide the same results.


they did.


the values that i used in my evaluation were:


m = 52
a = 3
b = 6


you can use any other values you like, but don't make the numbers so large that your calculator can't handle them.
if you get an overflow error, then your numbers were too large for the calculator to handle.


the calculator i used is the ti-84 plus.


here's a reference on exponent arithmetic.


<a href = "https://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents" target = "_blank">https://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents</a>