Question

Solve this equation, and show work. worth 40 points.

Answer 1

Answer:

$b=-3$

Step-by-step explanation:

We have:

$25^b\cdot 125^{b+2}=125^b$

Notice that 125 is the same as 5³. So:

$25^b\cdot ((5)^3)^{b+2}=((5)^3)^b$

Also, 25 is the same as 5². So:

$((5)^2)^b\cdot ((5)^3)^{b+2}=((5)^3)^b$

Power of a power property:

$5^{2b}\cdot 5^{3(b+2)}=5^{3b}$

Power of a product property:

$5^{2b+3(b+2)}=5^{3b}$

Since they have the same base, the exponents are equal. So:

$2b+3(b+2)=3b$

Solve for b. Distribute on the left:

$2b+3b+6=3b$

Combine like terms on the left:

$5b+6=3b$

Subtract 5b from both sides:

$6=-2b$

Divide both sides by -2. So, the value of b is:

$b=-3$

And we're done!

Answer 2

Answer:

b = - 3

Step-by-step explanation:

Please see the attachment below of the following work.

Thanks! Can I have BRAINLIEST please?

Hope this helps!