Question

Can you please help me in this quick question? I'm so mad at it no matter what I do it's wrong :(

Write the expression as a monomial in its standard form.
(–0.2b^6)^3*5b

It's kind of confusing when I write it like that without the exponents and stuff but yeah please help thanks

Answer 1

`-0.04b^(19)`

Explanation:

We have the expression
`(-0.2b^6)^3* 5b` and we want to rewrite/simplify this to a monomial (only one term).

First, let's expand. We can use the power of a product exponent property, where
`(ab)^x=a^xb^x`

We have:

`(-0.2b^6)^3* 5b`

Using the above property, this will be:

`=(-0.2)^3(b^6)^3*5b`

(-0.2) cubed is -0.008. So, this becomes:

`=-0.008(b^6)^3* 5b`

We can now use the power of a power property, where
`(x^a)^b=x^(ab)`.

Therefore, this will give us:

`=-0.008b^(6* 3)* 5b`

Evaluate:

`=-0.008b^(18)* 5b`

Notice that 5b is the same as 5 times b to the first power. So:

`=-0.008* b^(18)*5* b^1`

We can rearrange this to get:

`=-0.008* 5* b^(18)* b^1`

When we multiply exponents with the same base, we will simply add the exponents. -0.008 times 5 is -0.04. Therefore, this yields:

`=-0.04b^(18+1)\\=-0.04b^(19)`

Therefore, our final answer is
`-0.04b^(19)`.

And this is indeed a monomial since this only has one term.