Can anyone explain this problem with steps:

Question

(49/25)^3/2

Answer 1

Happy to see that you said "explain".  This means you truly want to learn.

 

First notice the term in parenthesis is a perfect square.  So we can rewrite this as

 

[(7/5)²]^(3/2)

 

 

Next, we can apply the rules of exponents.  Multiply the exponents.

 

(7/5)³

 

 

Complete the rest.

Answer 2

In re-writing the equation as:

 

  √(49)³

    ----- -             Since the end result is simplifying, I would do

    (25)³               2 steps at one time: solving the cube and factoring to get:

 

 

 √(7x7)(7x7)(7x7)

    --------------------- -    This looks a little better. Now since you are looking

    (5x5)(5x5)(5x5)         for the square root, you want the factors that

                                     repeat in sets of 2. These become the

                                     "representatives" of your square root,

                                     and for EACH PAIR, are multiplied.

                                     So there are three pairs of 7 (7x7x7), and

                                     3 pairs of 5 (5x5x5). There is nothing left

                                     after the pairs, so the solution would be:

 

              343

             ------

              125

 

Go Get Your "A".

 

Thanks.

Answer 3

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Answer 4

Since both 49 and 25 are perfect squares, I suggest taking the square root first, and then elevation to the 3rd power:

 

(49/25)^(3/2) = [(49/25)^(1/2)]^3

 

= [49^(1/2) / 25^(1/2)]^3

 

= (7/5)^3 = 7^3 / 5^3 = 343/125

Answer 5

Angelia,

 

To get started, remember that a^m/n is equal to both ⁿ√(a^m) AND (ⁿ√a)^m.

You choose the one to use to make the steps simpler.

 

Remember that √49 = 7 and √25 = 5. I suggest finding the answer using the second formula.

 

(49/25)^3/2 = (√(49/25))³ = (7/5)³ = 7³/5³ = 343/125.

 

The answer is 343/125.

 

Just to note: if you used the first formula, you would need to find √((49/25)³) = √(117649/15625), which is a LOT harder than the way I showed you. This is the reason there are two different ways to do this problem. You choose the formula which makes it easiest for you.

 

I hope this helps you. Reply back if you need to.

Answer 6

Hi Angelia!

So for this exponent related problem you first need to know what fractions do as exponents. If you had 16^(1/2) that would equal the square root of 16. If you had 8^(1/3) that would equal the cube root of 8. Do you see how the fraction and the root are related. The denominator of the fraction determines which root. Writing a root as a fraction or a fraction exponent as a root is just a different way to write the problem. The problem you have can be re-written as the square root of (49/25)^3. The nice thing is that because of the way exponent rules work we could either take 49 and 25 to the power of 3 and then take the square root or we could do that the other way around. I think it is easier in this case to take the square root first. So the square root of 49/25 is 7/5. Then if you cube 7/5 you get 343/125. 

Hope this helps!