Question

Would someone that knows how to simplify exponents tell me if my homework answers are correct?

Here is the first one and my answer:

16^-5/4 my answer 1/32

Second question:

(1/4) ^3/2 my answer: 1/128

Am I correct on both questions? If not please lead me to the answers. Thanks!

Answer 1

Help! How do I figure the second one?

Answer 2

The first answer is correct.

The second answer is incorrect. To raise a number to the 3/2 power, we take the square root of it, and then cube that answer (it actually doesn't matter what order you do these in). So, \[.25^{3/2} = (\sqrt{.25})^3\]The square root of 1/4 is 1/2, so
\[(\sqrt{.25})^{3} = (1/2)^{3} = 1/(2^{3}) = 1/8\]
So our answer is 1/8.

Answer 3

Thank you Vinny, I am copying your strategy for my notes. Can you tell me if this answer is correct for this problem? √50xz^10 my answer 3. ^5√(2 √xz^10

Answer 4

The three is not part of the answer.

Answer 5

The way you typed the question and answer there is a little unclear, could you try using the equation button below the box you're typing in to set it up a little more clearly?

Answer 6

Here is the question:

√(50xz^10)

Answer 7

my answer is

Answer 8

^5√(2 √(xz^10

Answer 9

if that a square root or 5th root ?

Answer 10

ok, so the question is
\[\sqrt{50x(z^{10})}\]

You can pull out a 5 in front, which I see you did. So now you have
\[\sqrt{2x(z^{10})}\]

But theres one more step you can do. You have z^10 which you can take the square root of. When you square root something, you are halving the exponent, so the square root of z^10 is z^5, which you can pull in front, so your final answer is
\[5(z^{5})\sqrt{2x}\]

Answer 11

I understand and will copy your notes! You deserve a medal, here you go!

Answer 12

Thank you, I'm glad I could help.

Answer 13

You have definitely helped, I get really nervous with homework assignments!

Answer 14

I have a new one can you help me with this one? I have never seen this in class before.

(5√3-2√6) (2√6+√3)

Answer 15

The answer in the calculator is 24√2-9

Answer 16

The equation states to multiply.

Answer 17

Ok. We need to mutlply these two together, and we will use the FOIL method. Are you familiar with this method? It's a rather simple way to multiply two pieces of the form (a+b)(c+d). When we foil this out we get -

First - (5√3)(2√6) = 10√18 = 30√2
Outside - (5√3)(√3) = 5√9 = 15
Inside - (-2√6)(2√6) = -4√36 = -24
Last - (-2√6)(√3) = -2√18 = -6√2

So our final answer is
30√2 + 15 - 24 - 6√2

Answer 18

We can simplify this to 24√2 - 9.

Answer 19

It does ask to simplify as much as possible! Thank your for writing the steps!

Answer 20

Are you up for a harder equation it say to simplify?

Answer 21

a^5/2 a^-1/2/a^1/3 the a^1/3 is the denominator to rest is the numerator.

Answer 22

Ok, so it looks like this?
\[\frac{ a^{5/2} \times a^{-1/2} }{ a^{1/3} }\]

Answer 23

The denominator is a ^1/3 Now there was not any implication to multiply no x or dot to imply multiplication, it states to simplify. I got a^25/6/2

Answer 24

If they're next to each other in the numerator then they are multiplied. When we multiply, we add the exponents, when we divide, we subtract them.
\[\frac{ a^{(5/2)-(1/2)} }{ a^{1/3} } = \frac{ a^{4/2} }{ a^{1/3} } = a^{4/2 - 1/3} = a^{5/3}\]

Answer 25

Clearly I am algebra challenged now does it matter that the negative symbol is next to -1/2 it is not outside? I mean would that change the answer? Thank you for your help!

Answer 26

Shouldn't it be -(-1/2) and would that change the answer?

Answer 27

-(1/2) and -1/2 are equivalent. In the first fraction I put, you're actually adding 5/2 + (-1/2) but I skipped a step and wrote it as 5/2 - 1/2. Sorry if I confused you.

Answer 28

Hi Vinny, I was all ready confused. In the example the denominator is multiplied with the denominator of the numerator, wouldn't that be 3 x 2 = 6?

Answer 29

The example only has one fraction at the top so it is not completely similar and is throwing me off!

Answer 30

The base is always the same, so when we multiply together, we add the exponents. The numerator had some multiplication so thats why we add the exponents. After I simplified the numerator, we need to evaluate a^(4/2) / a^(1/3). Since we are dividing, we must subtract the exponents. 4/2 - 1/3 is equal to 5/3, which becomes our exponent.

Answer 31

So the final answer is a^5/2 correct?

P.S. How would I write b^4/7 as a radical expression?

Answer 32

The final answer would be a^5/3. This is assuming I understood the question you posed to me correctly.

When we have a fractional exponent, the number of the exponent is the power, and the denominator is the root. So, for b^(4/7) we have
\[b^{4/7} = (\sqrt[7]{b})^{4}\]

Answer 33

Thank you for that because I wrote it backwards. How do you process the steps for this?

Answer 34

Do I need the parentheses? and is this correct: (7√b )^4

Answer 35

Thank you for the explanation. I have asked this question in an e-mail to my teacher and never got a response. Thank you for that!

Answer 36

The parenthesis are actually not necessary because the following are all equivalent:
\[b^{4/7} = (\sqrt[7]{b})^{4} = \sqrt[7]{(b^{4})}\]

Answer 37

Last question how would I simply this?

√50/32 The radical symbol stretches the length of the fraction.

Answer 38

The calculator shows 5/16√2

Answer 39

or 5/4

Answer 40

If the radical stretches over the whole fraction, then the answer can be found by finding the radical of the top over the radical of the bottom.
\[\sqrt{50/32} = \sqrt{50} / \sqrt{32} = \frac{ 5\sqrt{2} }{ 4\sqrt{2} } = \frac{ 5 }{ 4 }\]

Answer 41

Thank you for showing your work! I am finding that I am actually learning in this format! Thank you for being such a good teacher!

Answer 42

Please check my first equation:

8w√(48wu^2 –u √75^3)

my answer: 27uw√3w

Answer 43

Vinny I hope that you do not mind checking homework with me. I forgot to ask if you had the time!

Answer 44

Ok, does it look like this?
\[(8w)\sqrt{48wu^{2} - (u)\sqrt{75^3}}\]

Answer 45

There are two radical signs: 8w√48wu^2 -u √75^3

Answer 46

it is 75 cubed

Answer 47

75w^3

Answer 48

Hows this -
\[8w \sqrt{48wu^2} - \sqrt{75w^3}\]

Answer 49

Hows this -
\[8w \sqrt{48wu^2} - \sqrt{75w^3}\]

Answer 50

There is a -u in the center but all everything else is perfect!

Answer 51

Vinny is 27uw √3w correct?

Answer 52

Ok I see what you mean. Sorry for the delay, I'm tackling way too many questions at once.

\[8w \sqrt{48wu^2} - u\sqrt{75w^3}\]

We can pull out a 16 from the 48, which will give us a 4 in front and leave a 3 in the radical. We can also square root the u^2. From the second radical pull out and square root the 25.

\[32wu \sqrt{3w} - 5u\sqrt{3w^3}\]

Now, we can pull out a w^2 and square root it. Simplify and we're done.

\[32wu \sqrt{3w} - 5wu\sqrt{3w} = 27uw \sqrt{3w}\] Looks good!

Answer 53

Yeah! My last question, and I just want to know if my answer is correct.

2. Rationalize the denominator and simplify: √5/√13 answer √65/13

Answer 54

Multiply top and bottom by √13, and you're done. You've got it.

Answer 55

Ok, I multiplied 5 x 13 and got 65 squared over 13, am I correct?

Answer 56

Yep, thats perfect. You definitely have a good handle on this stuff.

Answer 57

Awwwww! You make me feel so much better because I am seriously a novice!

Answer 58

With a little practice you can quickly become a pro. You could look online for some more practice problems if you'd like to build your confidence. I think I'm signing off for the night though.

Answer 59

One more check if you do not mind? If not THANK YOU!

Checking this question: Solve :(v-1)^3-88=0

answer v=1+2^3√11

Answer 60

THANKS AGAIN VINNY FOR ALL OF YOUR HELP!

Answer 61

The answer that you should be getting is
\[\sqrt[3]{88} +1\] By adding 88 to both sides, cube rooting both sides, and adding 1 to both sides.

I'm signing off for the night. If I've been helpful and you think I deserve it, I would greatly appreciate you adding me as a fan or even writing a testimonial on my profile. I'm glad to help.

Answer 62

What is the number outside of the radical symbol?

Answer 63

Thats a 3, it's the cube root of 88. You could pull out an 8 and cube root it. I think thats what you meant to say it was just typed a little inaccurately.

Answer 64

Ok I am a fan and you have been great. When I finish my homework I will write a testimonial because you not only guided me, you helped to teach me concepts I had a hard time learning in the classroom. That's a good testimony! HAVE A GREAT EVENING!

Answer 65

Thanks! Have a great weekend.

Answer 66

I WILL NOW THANKS TO YOU!

Hope to work with you again! Tuiti