Question

Multiply the monomials: d a^2x^5b, −0.6axb^2 and 0.6a^2b^3

Answer 1

`-0.36a^5b^6x^6.`

Explanation:

Given:

a²x⁵b, −0.6axb² and 0.6a²b³

Required

Find their product

The product of a²x⁵b, −0.6axb² and 0.6a²b³ is as follows:

`a^2x^5b * -0.6axb^2 * 0.6a^2b^3`

Split individual monomial

`a^2*x^5*b * -0.6*a*x*b^2 * 0.6*a^2*b^3`

Bring like terms together

`-0.6 * 0.6 * a^2 * a * a^2 *b *b^2 * b^3 *x^5*x`

For ease of multiplication, group each like terms using brackets

`(-0.6 * 0.6) * (a^2 * a * a^2) * (b *b^2 * b^3) *(x^5*x)`

Using law of indices;

Which states that;
`m^a * m^b = m^(a + b)`

The expression becomes:

`(-0.36) *(a^(2+1+2)) * (b^(1+2+3)) * (x^(5+1))`

`-0.36 * a^5 * b^6 * x^6`

Multiply the above expression

`-0.36a^5b^6x^6.`

Hence;

The product of a²x⁵b, −0.6axb² and 0.6a²b³ is equivalent to
`-0.36a^5b^6x^6.`