How do you simplify #(root3(6)*root4(6))^12#?

Answer 1

#(root3(6)*root(4)6)^12=6^7=279936#

We need the rules:

Using #color(red)star#, we see that:
#(root3(6)*root(4)6)^12=(6^(1/3)*6^(1/4))^12#
Now using #color(green)star#, this becomes:
#(6^(1/3)*6^(1/4))^12=(6^(1/3+1/4))^12#
Note that #1/3+1/4=4/12+3/12=7/12#.
#(6^(1/3+1/4))^12=(6^(7/12))^12#
Now using #color(blue)star#, we multiply the exponents:
#(6^(7/12))^12=6^(7/12xx12)#
And we see that #7/12xx12=7#:
#6^(7/12xx12)=6^7#
All of which we did without a calculator! For an expanded value, we could plug in #6^7# into a calculator to see that #6^7=279936#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To simplify the expression (root3(6)*root4(6))^12, we can first simplify the individual square roots. The square root of 6 can be written as 6^(1/2) and the fourth root of 6 can be written as 6^(1/4).

Next, we can simplify the expression inside the parentheses by multiplying the exponents. (6^(1/2) * 6^(1/4))^12 becomes 6^((1/2)(12)) * 6^((1/4)(12)).

Simplifying further, we have 6^(6) * 6^(3).

Finally, we can combine the two terms by adding the exponents. 6^(6+3) simplifies to 6^9.

Therefore, the simplified expression is 6^9.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7