what is ^3√54 simplified
^3√54 simplified is 3√2.
To simplify the cube root of 54 (^3√54), we need to find the perfect cube that can divide 54.
Step 1: Prime factorize 54.
54 = 2 * 3 * 3 * 3
Step 2: Group the factors in sets of three.
54 = 2 * (3 * 3 * 3)
Step 3: Simplify each set of three factors.
54 = 2 * (3^3)
Step 4: Rewrite the expression.
^3√54 = ^3√(2 * (3^3))
Step 5: Simplify the cube root.
^3√54 = 3√(2) * 3√(3^3)
Step 6: Evaluate the cube root of 3^3.
^3√54 = 3√(2) * 3^(3/3)
Step 7: Simplify the exponent.
^3√54 = 3√(2) * 3^1
Step 8: Evaluate 3^1.
^3√54 = 3√(2) * 3
Step 9: Multiply the terms.
^3√54 = 3√(2 * 3)
Step 10: Simplify the expression.
^3√54 = 3√6
So, ^3√54 simplified is 3√6.
what is power of 3√54 simplified
To simplify the power of 3√54, we raise the cube root of 54 to a specific power.
Let's say the power is n.
(3√54)^n
Using the property of exponents, when we raise a power to another power, we multiply the exponents:
(3√54)^n = (3√(2 * 3))^n
Now, we can rewrite the expression using the properties of radicals:
(3√2 * 3)^n = (3 * (3√2))^n
Again, applying the rule of exponents:
(3 * (3√2))^n = 3^n * (3√2)^n
Now we have the simplified form of the expression. However, if you provide a specific value for n, we can calculate it for you.
To simplify the cube root of 54 (^3√54), we need to find the largest perfect cube that divides 54.
Since 27 is the largest perfect cube that divides 54 (27 * 2 = 54), we can simplify ^3√54 as ^3√(27 * 2).
Now, we can rewrite this expression as (^3√27) * (^3√2).
The cube root of 27 is 3 (since 3 * 3 * 3 = 27), so we have 3 * (^3√2).
Therefore, the simplified form of ^3√54 is 3 * ^3√2.