Question

X⁴ y⁹ sqrt[3] x¹⁰ y⁴ ? what is the simplest form of x sqrt; x⁹ * y⁹; x⁶ * y⁰ * root(x³ * y⁴, 3); x² = sqrt(x ² * y²) done

Answer 1

To simplify expressions with exponents, add exponents when multiplying like bases. Square and fourth roots can be expressed as fractional exponents. Cubing an exponential term involves multiplying its exponent by three.

Step-by-step explanation:

We are presented with several mathematical expressions involving exponents and roots that need to be simplified. To achieve the simplest form of an expression with exponents, you can add exponents when multiplying like bases, as shown in the reference xPx9 = x(p+q).

For radical expressions, the square root of a number can be expressed as a number to the power of 0.5, as seen in x² = √x. Similarly, taking the fourth root is the same as raising to the power of 0.25, which can also be achieved by taking the square root twice.

The cubing of exponentials is done by multiplying the exponent by 3. This is helpful for problems where you need to cube an exponential term.