Hello, maddy*1!
\(\displaystyle \L(8a^4b^6)(9a^3b^7)\)
Sort the factors like this: \(\displaystyle \L\,8\,\cdot9\,\cdot\,a^4\,\cdot\,a^3\,\cdot\, b^6\,\cdot\,b^7\)
\(\displaystyle \;\;\)(Do it "in your head"; you
don't have to write this out.)
Multiply the coefficients (normal arithmetic): \(\displaystyle \L\,8\,\times\,9\:=\:72\)
and multiply the variables (Use the Multiplication Rule for exponents:
\(\displaystyle \L\;\;\;a^4\,\cdot\,a^3\:=\:a^{(4+3)}\:=\:a^7\;\;\;\;\;b^6\,\cdot\,b^7\:=\:b^{(6+7)}\:=\:b^{13}\)
\(\displaystyle \text{Answer: }\L\;72a^{^7}b^{^{13}}\)
