Question

Which equations are correct? Select each correct answer.

3b3(−2b4)=−6b12
5x3(6x4)=30x7
4c4(3c2)=12c8
5y4(2y5)=10y9

Answer 1

The answer to the question is the second and the fourth equations

Answer 2

Answer: The correct equations are

`(b)~5x^3(6x^4)=30x^7,\\\\(d)~5y^4(2y^5)=10y^9.`

Step-by-step explanation: We are given to select the correct equations from the following :

`(a)~3b^3(-2b^4)=-6b^(-12),\\\\(b)~5x^3(6x^4)=30x^7,\\\\(c)~4c^4(3c^2)=12c^8,\\\\(d)~5y^4(2y^5)=10y^9.`

We will be using the following property of exponents :

`a^b* a^c=a^(b+c).`

We have

For equation (a)

`L.H.S.=3b^3(-2b^4)=-6b^(3+4)=-6b^7\\eq-6b^(12)=R.H.S.`

So, this equation is not correct.

For equation (b)

`L.H.S.=5x^3(6x^4)=30x^(3+4)=30b^7=R.H.S.`

So, this equation is CORRECT.

For equation (c)

`L.H.S.=4c^4(3c^2)=12c^(4+2)=12c^6\\eq12c^8=R.H.S.`

So, this equation is not correct.

For equation (d)

`L.H.S.=5y^4(2y^5)=10y^(4+5)=10y^9=R.H.S.`

So, this equation is CORRECT.

Thus, the correct equations are

`(b)~5x^3(6x^4)=30x^7,\\\\(d)~5y^4(2y^5)=10y^9.`