Question

I am trying to help my daughter with summer algebra and can't remember what steps to solve (a to the 5th times bsquared all the the 3rd divided by a to the 7th and b to the 3rd. We know the answer is a to the 8th times b 3rd. Would love help!

Answer 1

Remember when you raise a power to a power, you multiply exponents:
\[\large (a^5b^2)^3 = a^{5\cdot 3}b^{2\cdot 3} = a^{15}b^{6}\]

And when you divide powers of the same base you subtract their exponents.

\[\large \frac{ a^{15}b^{6}}{a^7b^3} = a^{15-7}b^{6-3} = a^8b^3\]

Answer 2

a^5 is notation for "a to the 5th"

b^2 is notation for "bsquared"

(a^5 b^2)^3 is likewise easier to read mathematically ..

just saying :)

Answer 3

at times people omit the "^" part and its just as sensible for the most part