Trouble with answer to question: A cyclist travels 4b^2c^1/2 miles in 3b^2c hours. What is her average speed?

[mathsenjoy]

"A cyclist travels 4b^2c^1/2 miles in 3b^2c hours. What is her average speed?"

My calculation so far is in the photo attached. I understand b^2/b^2=1 because any number to power 0 is 1(except 0).
What i don't understand is how the answer in the textbook is 4 / 3c^1/2 mph
Why in the answer is c now at the bottom?
I also do not understand how c^1/2 / c =c^1/2
since i thought a number without a power stated is to the power 1 e.g 5 is 5^1, therefore c is the same as c^1 so i thought i had to minus the powers on C when dividing exponents. Yes I am very confused and if someone can clear this up I would be grateful.

As I mention in all my posts I missed some formal education growing up.

 

[skeeter]

change the addition signs to multiplication signs since all values and variables are being multiplied in both the numerator and denominator

 

[Otis]

I understand b^2/b^2=1 because any number to power 0 is 1

Hi mathsenjoy. You're thinking about b^0=1 because you'd applied the following property of exponents to b^2/b^2, yes?

N^A / N^B = N^(A–B)

Therefore: b^2/b^2 = b^(2–2) = b^0 = 1

What do you get, when you apply the same property to c^(1/2) / c ?

Or, perhaps, your toolkit is missing this other property.

N^(-A) = 1 / N^A

In other words, a negative exponent denotes the reciprocal of a power. For example:

2^3 = 8

2^(-3) = 1/(2^3) = 1/8

the answer in the textbook is 4 / 3c^1/2

Correct — when typed with proper grouping symbols (shown below). Here's some info about grouping symbols. If we strictly follow the Order of Operations, then the typed expression 4 / 3c^1/2 means [imath]\frac{4}{3} \cdot \frac{3c}{2}[/imath] instead of [imath]\frac{4}{3\sqrt{c}}[/imath], due to missing grouping symbols. We use grouping symbols with the Associative Properties and also when we want to change the Order of Operations.

In your case, we need to add grouping symbols to show that 1/2 is the exponent and that 4 is in the numerator with everything else in the denominator.

When an exponent is more than one character, we enclose the exponent within grouping symbols.

c^(1/2)

When a denominator is more than one character, we almost always need to enclose the entire denominator within grouping symbols.

4/[3c^(1/2)]

The answer could be expressed as 4c^(-1/2)/3, too.

Please ask questions, if I wrote anything that you don't understand.

PS: In the last expression of your work, the fractions ought to be multiplied together, instead of added.
[imath]\;[/imath]