Help with Algebra 2 Please

Question

Alright so the question is If m > 0, the expression 2(sqrt of m) to the power of 3 over the fourth root of m can be rewritten in the form 2m to the power of a, where a is a fraction. what is the value of a?

Answer 1

I think you are describing:

Remember that you can switch back and forth between radicals and exponents by using the index of the radical (the "root power") as the denominator of the exponent. For example the fourth root of m is the same as m raised to the 1/4 power.

So, (sqrt of m) to the power of 3 is m^3/2

So another way to write the expression " 2(sqrt of m) to the power of 3 over the fourth root of m" is:

2m^3/2/m^1/4

Then, an important rule of exponents is that when two exponential expression with the same base that are being divided can be simplified by subtracting the exponents, in other words b^m/bⁿ = b^m-n.

So we can simplify the expression 2m^3/2/m^1/4 to be 2m^3/2-1/4 but to subtract the exponents, we need a common denominator (which is 4) so it becomes:

2m^6/4-1/4 = 2m^5/4 meaning a = 5/4