Question

Simplify the expression ab^3/a^4b + (c^2)^3.

A.b^3 c^6/a^3
B. b^2 c^5/a^3
C. b^2/a + c
D. b^2/a^3 + c^5
E. B^2/a^3 + c^6

Answer 1

Hello!

Answer:

`\Large \boxed{\sf ( b^2)/(a^3) +c^6}`

Explanation:

→ We want to simplify this expression:

`\sf ( ab^3)/(a^4b) + (c^2)^3`

→ Simplify ab³/a⁴b:

→ Simplify b³/b:

`\sf (b^3)/(b) = b^2`

→ Simplify a/a⁴:

We know that
`\sf (x^a)/(x^b)` is equal to
`\sf (1)/(x^(b-a) )`

`\sf (a)/(a^4) = (1)/(a^(4-1) ) = (1)/(a^3)`

→ So:

`\sf (1 * b^2)/(a^3) = (b^2)/(a^3)`

→ Simplify (c²)³:

We know that
`\sf (x^a)^b` is equal to
`\sf x^(a* b)`

So:

`\sf (c^2)^3 = c^(3* 2) = c^6`

→ Simplify the expression:

`\boxed{\sf (b^2)/(a^3) + c^6}`

Conclusion:

The expression ab³/a⁴b + (c²)³ is equal to b²/a³ + c⁶.

So the answer is e).