Question

Which equations are correct? Select each correct answer.

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 :

$a^b\times a^c=a^{b+c}.$

We have

For equation (a)

$L.H.S.=3b^3(-2b^4)=-6b^{3+4}=-6b^7\neq-6b^{12}=R.H.S.$

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)

$L.H.S.=4c^4(3c^2)=12c^{4+2}=12c^6\neq12c^8=R.H.S.$

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

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