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Answer:
b: 7^18 / 7^9
c: (7^3)^3
e: 7^4 * 7^5
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
(a^b)/(a^c) = a^(b-c)
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The given expression is ...
[tex]7^8\cdot7=7^8\cdot7^1=7^{8+1}=7^9[/tex]
The offered alternatives are ...
[tex]\textbf{a: }7^3\cdot7^3=7^{3+3}=7^6\quad\textbf{not equivalent}\\\\\textbf{b: }\dfrac{7^{18}}{7^9}=7^{18-9}=7^9\quad\textbf{equivalent}\\\\\textbf{c: }(7^3)^3=7^{3\cdot3}=7^9\quad\textbf{equivalent}\\\\\textbf{d: }7^4+7^5=7^4(1+7)=8\cdot7^4\quad\textbf{not equivalent}\\\\\textbf{e: }7^4\cdot7^5=7^{4+5}=7^9\quad\textbf{equivalent}[/tex]
