Personally I prefer to convert roots to fractional powers for this kind of problem. cube root of x squared is x2/3, and square root of x is x1/2. Adding the exponents, you get x2/3 times x1/2 = x7/6, that is, the sixth root of x to the seventh power - where it doesn't matter whether you take the sixth root first, or raise to the sevents power first. Alternatively, you can convert all roots to sixth roots, and multiply - and of course, get the same result.
The square root of x to the 10th power is x to the 10th power raised to the 1/2 power, which simplifies to x to the 10/2 power. This further simplifies to x to the 5th power. Therefore, the square root of x to the 10th power is x to the 5th power.
X to the 3rd power
You divide the exponent by 2 The square root of a number is that number to the 1/2 power So for examle square root of x cubed (x^3) is x^3 to the half power =x^3/2 (x to the 3/2 power)
The equation is equivalent to 'x to the power of 4 thirds' times 'x to the power of 2.5'. Multiplying them together, we simply add the powers, giving 'x to the power of 23/6' or the 'sixth root of x to the power of 23'.
It is x to the sixth power.
The equation is equivalent to 'x to the power of 4 thirds' times 'x to the power of 2.5'.Multiplyling them together, we simply add the powers, giving 'x to the power of 23/6' or the 'sixth root of x to the power of 23'.
The square root of x squared is x, or x to the first power.
Personally I prefer to convert roots to fractional powers for this kind of problem. cube root of x squared is x2/3, and square root of x is x1/2. Adding the exponents, you get x2/3 times x1/2 = x7/6, that is, the sixth root of x to the seventh power - where it doesn't matter whether you take the sixth root first, or raise to the sevents power first. Alternatively, you can convert all roots to sixth roots, and multiply - and of course, get the same result.
The square root of x = x to the power of a half
The square root of x to the seventeenth power is x to the eighth and a half power. If x is negative, the answer is imaginary.
The square root of x to the 10th power is x to the 10th power raised to the 1/2 power, which simplifies to x to the 10/2 power. This further simplifies to x to the 5th power. Therefore, the square root of x to the 10th power is x to the 5th power.
the square root of x8 is x4
X to the 3rd power
Square root of x
The square root of x12 is x6 .
3/(4*square root(x)) ....Mukesh