Question

Simplify this expression (xto the power of 2) to the power of 3+( xto the power of 3) to the power of 2

Answer 1

The expression (x^2)^3 + (x^3)^2 simplifies to 2x^6 by applying the rule for powers to an exponent, multiplying the exponents, and then adding the like terms.

Step-by-step explanation:

To simplify the expression (x^2)^3 + (x^3)^2, we apply the rule of powers to an exponent, which means multiplying the exponents. For the first part (x^2)^3, we multiply the exponents 2 and 3 to get 2*3 = 6, so (x^2)^3 simplifies to x^6. Similarly, for the second part (x^3)^2, we multiply the exponents 3 and 2 to get 3*2 = 6, so (x^3)^2 simplifies to x^6. The entire expression thus simplifies to x^6 + x^6, which can be further simplified to 2x^6 since we are adding two identical terms together.

Answer 2

The expression (x^2)^3 + (x^3)^2 simplifies to 2x^6, by applying the rules for squaring and cubing exponentials which involve multiplying the exponents by the respective power (2 and 3).

Step-by-step explanation:

To simplify the expression (x^2)^3 + (x^3)^2, we apply the rules of squaring of exponentials and cubing of exponentials. When squaring an exponential expression, you square the digit term in the usual way and multiply the exponent by 2. Similarly, when cubing, you cube the digit and multiply the exponent by 3.

For the first term, (x^2)^3, we multiply the exponents: 2*3 = 6, resulting in x^6. For the second term, (x^3)^2, we do the same: 3*2 = 6, resulting in x^6. So, the expression simplifies to x^6 + x^6.

As both terms are like terms (they have the same base and exponent), they can be added together, resulting in 2x^6.