Answer:
[tex]-0.04b^{19}[/tex]
Step-by-step explanation:
We have the expression [tex](-0.2b^6)^3\times 5b[/tex] 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 [tex](ab)^x=a^xb^x[/tex]
We have:
[tex](-0.2b^6)^3\times 5b[/tex]
Using the above property, this will be:
[tex]=(-0.2)^3(b^6)^3\times5b[/tex]
(-0.2) cubed is -0.008. So, this becomes:
[tex]=-0.008(b^6)^3\times 5b[/tex]
We can now use the power of a power property, where [tex](x^a)^b=x^{ab}[/tex].
Therefore, this will give us:
[tex]=-0.008b^{6\times 3}\times 5b[/tex]
Evaluate:
[tex]=-0.008b^{18}\times 5b[/tex]
Notice that 5b is the same as 5 times b to the first power. So:
[tex]=-0.008\times b^{18}\times5\times b^1[/tex]
We can rearrange this to get:
[tex]=-0.008\times 5\times b^{18}\times b^1[/tex]
When we multiply exponents with the same base, we will simply add the exponents. -0.008 times 5 is -0.04. Therefore, this yields:
[tex]=-0.04b^{18+1}\\=-0.04b^{19}[/tex]
Therefore, our final answer is [tex]-0.04b^{19}[/tex].
And this is indeed a monomial since this only has one term.
