Simplify the following: (54^1/4)/ (6^3/4)(12^-1/2)
To simplify the given expression `(54^(1/4))/(6^(3/4))(12^(-1/2))`, let's simplify each term separately.
Step 1: Simplify `54^(1/4)`:
To simplify a number raised to a fractional exponent, we take the nth root of the number. In this case, `54^(1/4)` means finding the 4th root of 54.
The 4th root of 54 is approximately 2.803.
Step 2: Simplify `6^(3/4)`:
Similarly, `6^(3/4)` represents finding the 4th root of 6 raised to the power of 3.
The 4th root of 6 is approximately 1.565.
Step 3: Simplify `12^(-1/2)`:
`12^(-1/2)` means finding the reciprocal of the square root of 12.
The square root of 12 is approximately 3.464, so the reciprocal is 1/3.464 or approximately 0.289.
Now, simplify the expression by substituting the simplified values:
(2.803)/(1.565)(0.289)
Step 4: Evaluate the expression:
Multiply 1.565 by 0.289:
1.565 * 0.289 ≈ 0.452
Finally, divide 2.803 by 0.452:
2.803 / 0.452 ≈ 6.196
Therefore, the simplified value of the expression (54^(1/4))/(6^(3/4))(12^(-1/2)) is approximately 6.196.