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anonymous
 one year ago
How do you solve this problem? Please explain!
anonymous
 one year ago
How do you solve this problem? Please explain!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(4a ^{5/3})^{3/2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It says to simplify in this problem

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1basic rule is \(\large (b^n)^m = b^{n \times m}\) because it's \(b^n \times b^n \times b^n ......\) m times. so \(\large (a. \ b^n)^m = a^m \ . \ b^{n \times m}\) But you can go at this in a number of ways; and you might wish to try this approach: \(\large (4a^{5/3})^{3/2} = \sqrt{4a^{5/3} \ * 4a^{5/3} \ * 4a^{5/3} }\) it's not the immediate solution, you will get that by looking up the exponent rules as posted above, but it might help get you get comfortable with these kind of questions.....maybe under the \(^{3/2}\) umbrella you are cubing and square rooting....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would I multiply the numbers inside the square root?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1well, imagine the square root is not there. jut multiply those out as you normally would: \(4 a^{5/3} \times 4 a^{5/3} \times4 a^{5/3} \) we'll worry about the square root sign after we have done that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. When you are multiplying exponents you have to add them right?

phi
 one year ago
Best ResponseYou've already chosen the best response.1when multiplying the same base , you add the exponents.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So without the square root it equals 4a^5?

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you remember that x*x*x is x^3 but x is x^1 and x*x is x^2 you get the example x^1 * x^2 = x^3 (that is how I remember this rule)

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, but you also have 4*4*4 to do

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1nah you also have 4 x 4 x 4!!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1fine i'll leave it to @phi you are in great hands!! good luck

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then it would equal 8a.....how would I square root the 5?

phi
 one year ago
Best ResponseYou've already chosen the best response.1a^5 is a*a*a*a * a we can do square root of a^4 (it is a*a or a^2) square root of the "extra" a is either sqr(a) or a^1/2

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \sqrt{64 a^4 } \sqrt{a} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the answer is \[8a \sqrt{a}\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So that would be simplified?

phi
 one year ago
Best ResponseYou've already chosen the best response.1they probably want you to use exponents, so write sqr(a) as a^(1/2)

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, and though it looks a bit weird, we are multiplying the same base. (the a) so we add the exponents. you get 2.5 but generally people write it as an improper fraction

phi
 one year ago
Best ResponseYou've already chosen the best response.1in other words, 2+ 1/2 is 4/2 + 1/2 = 5/2 and people write \[ 8 a^\frac{5}{2} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you are doing a lot of this, I would use the "fast way" \[ (b^n)^m = b^{n \cdot m} \] for example \[ (4^1 \cdot a ^\frac{5}{3})^\frac{3}{2} \] becomes \[ 4^\frac{3}{2} \cdot a^{\frac{5}{3}\cdot \frac{3}{2} }\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1notice the expoinet of a is 5*3/(3*2) which simplifies to 5/2 to find what 4^3/2 is, we have to do either \[ \left( 4^\frac{1}{2}\right)^3 = 2^3 = 8 \] or \[ \left( 4^3\right)^\frac{1}{2}= 64^\frac{1}{2} = 8 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh that makes sense.

phi
 one year ago
Best ResponseYou've already chosen the best response.1if it doesn't , doing a dozen problems will be tedious.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you happen to know how to do this problem? How do you make both numbers have the same base? \[(5a ^{2/3})(4a ^{3/2})\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1you are multiplying 4 "things" 5* a^(2/3) * 4 * a^(3/2) and you can switch the order: 5*4 * a^(2/3) * a^(3/2) does that help to know how to tackle this ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think so. I got 20 as my final answer.

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes 4*5 is 20 but you can't ignore the a's (but you can multiply them using "same base, add exponents" rule)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ya the a is \[a ^{1}\] So then the final answer would actually be 20a.

phi
 one year ago
Best ResponseYou've already chosen the best response.1when you *multiply* (like here) , and you have the same base, you *add* the exponents. in other words you get a^ new exponent and the new exponent is 2/3 + 3/2

phi
 one year ago
Best ResponseYou've already chosen the best response.1use a common denominator of 6 to get 4/6 + 9/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh....I was multiplying them again. So that would equal 13/6.

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. this stuff is confusing but try to remember the x*x = x^2 or (putting in the exponents) \[ x^1 \cdot x^1 = x^2\] as an example of adding the exponents

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay. So then it would equal \[20a ^{13/6}\]?
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