Question

I need help with math

Answer 1

The general equation is:

`(b^(2k)\cdot b^(3k))/(b^(4k))=b^k`

In the firs case, b = 5 and k = 1.

`\begin{gathered} (5^(2\cdot1)+5^(3\cdot1))/(5^(4\cdot1))=5^1 \\ (5^2+5^3)/(5^4)=5^{} \end{gathered}`

In the second case, b = 9 and k = 2.

`\begin{gathered} (9^(2\cdot2)+9^(3\cdot2))/(9^(4\cdot2))=9^2 \\ (9^4+9^6)/(9^8)=9^2 \end{gathered}`

In the third case, b = 2 and k = 3.

`\begin{gathered} (2^(2\cdot3)+2^(3\cdot3))/(2^(4\cdot3))=2^3 \\ (2^6+2^9)/(2^(12))=2^3 \end{gathered}`

In the fourth case, b = 3 and k = 4.

`\begin{gathered} (3^(2\cdot4)+3^(3\cdot4))/(3^(4\cdot4))=3^4 \\ (3^8+3^(12))/(3^(16))=3^4 \end{gathered}`