Question

(3x2)(−2x4) = 3(−2)x2∙4 = 6x8

Could you please find out what's wrong and say what should be there instead? The problem is : (3x to the power of 2 ) (-2x to the power of 4) = 3(-2)x to the power of 2.4 = 6x to the power of 8

Answer 1

The expression (3x2)(-2x4) was incorrectly simplified; it should be multiplied as -6, with the coefficients 3 and -2, and the exponents are added to get x6, leading to the correct answer: -6x6.

Step-by-step explanation:

The equation (3x2)(-2x4) has been incorrectly simplified. When we multiply two algebraic expressions, we need to multiply the coefficients together and add the exponents of the variables having the same base, according to the laws of exponents. In this case, we have:

• Multiplying the coefficients: 3 × (-2) = -6
• Adding the exponents: 2 + 4 = 6

The correct simplification of the given expression would therefore be: -6x6.

According to the rules of signs for multiplication, when two numbers with opposite signs are multiplied, the result will have a negative sign, which applies to the coefficients here. For the variable x, the exponents are added when multiplying like bases.

Answer 2

The correct answer is -6x⁶

Step-by-step explanation:

Given that:

`3x^2 ( - 2x^4 ) \\ \\ =3(-2)x^(2.4) \\ \\ = 6x^8`

From the second step above, using the law of indices the correct format should be

`= (3* -2)x^(2+4)`

So, the problem lies where we have 2.4, it is not supposed to be (2*4). It supposed to be 2+4 because the law of indices states that we multiply the index together and add their power.

Then the result of that yields

= -6x⁶

In the third step, they also omit the negative sign, when multiplying (3 * -2).

Thus, the correct answer is -6x⁶