Step-by-step explanation:
[tex]Use\ a^n\cdot a^m=a^{n+m}\\\\\bold{6.}\\\\7^5\cdot7^6=7^{5+6}=7^{11}\\\\\bold{7.}\\\\6^a\cdot6^v=6^{a+v}\\==========================\\Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\bold{8.}\\\\\dfrac{2^8}{2^7}=2^{8-7}=2^1=2\\\\\bold{9.}\\\\\dfrac{x^{56}}{x^{24}}=x^{56-24}=x^{32}[/tex]
[tex]=======================\\\\\bold{10.}\\\\\text{The scientific notation:}\ a\cdot10^k,\ \text{where}\ 1\leq a<10\ \text{and}\ a\in\mathbb{Z}:\\\\(9\cdot10^4)(8\cdot10^6)=(9\cdot8)(10^4\cdot10^6)=72\cdot10^{4+6}=72\cdot10^{10}\\\\=7.2\cdot10\cdot10^{10}=7.2\cdot10^{1+10}=7.2\cdot10^{11}\\\\\bold{11.}\\\\\text{The formula of an area of a rectangle:}\ A=wl\\\\w-width\\l-length\\\\\text{We have}\ l=7x+1\ \text{and}\ w=8x.\ \text{Substitute:}\\\\A=(7x+1)(8)\qquad\text{use the distributive property}\\\\A=(7x)(8x)+(1)(8x)\\\\A=56x^2+8x[/tex]
[tex]\bold{12.}\\\\(-8x)\cdot3x^2=(-8\cdot3)(x\cdot x^2)=-24x^{1+2}=-24x^3\\\\\bold{13.}\\\\(-11z)^0=1\\\\a^0=1\ \text{for all real numbers except 0}\\\\\bold{14.}\\\\Use\ a^{-n}=\dfrac{1}{a^n}\\\\14^{-4}=\dfrac{1}{14^4}[/tex]
