Simplify Sqareroot of 5^12 x 4 over 2 x 5^1/3

Question

I don’t understand this type of question. Can someone explain it to me in detail so I can understand? I don’t like asking for answers but I don’t understand this

Answer 1

Just like a simple division problem

5¹² *4²/(2¹*5^1/3)

=5¹²*2/5^1/3

when using exponents, division calls upon subtraction of exponents

5^(12-1/3)*2

=2*5^{(11 2/3)}

the squareroot( power 1/2)

(2*5^{(11 2/3)})^1/2

when using exponents, multiplication calls upon addition of exponents

2^(1+1/2)*5^{(11 2/3+1/2)}

⁼2^(3/2)*5^(73/6)

Answer 2

Hello Charlotte!

I assume this is the expression you're talking about?

√(5^12)(4)

_________

(2)(5^1/3)

If so, here is how you simplify it:

First, we want to solve the square root in the numerator. We do this by taking the square root of the values inside it - in this case, 5^12 and 4.

The square root of 5^12 = 5^6. The square root of 4 = 2.

We should get this:

(5^6)(2)

______

(2)(5^1/3)

Okay! This fraction looks much better without that square root symbol!

We see that there's a 2 in both the numerator and the denominator. We can cancel them out.

(5^6)(2) 5^6

______ → _______

(2)(5^1/3) 5^1/3

Both 5^6 and 5^1/3 have the same base: 5. We can simplify this expression by subtracting the exponents.

We get this:

5^( 6 - 1/3 )

(If you don't understand the last step, I recommend you to review how to simplify exponent expressions - this is a helpful link: https://www.purplemath.com/modules/simpexpo.htm)

Then, we subtract 1/3 from 6:

5 ^ (17/3)

This should be the solution to your problem! :) I hope this helps, and good luck!