Question

Which expressions are equivalent to 7^8 * 7? Select all that apply a: 7^3 * 7^3 b: 7^18 / 7^9 c: (7^3)^3 d: 7^4 + 7^5 e: 7^4 * 7^5

Answer 1

9514 1404 393

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 ...

  $7^8\cdot7=7^8\cdot7^1=7^{8+1}=7^9$

The offered alternatives are ...

  $\textbf{a: }7^3\cdot7^3=7^{3+3}=7^6\quad\textbf{not equivalent}\\\\\textbf{b: }\dfrac{7^{18}}{7^9}=7^{18-9}=7^9\quad\textbf{equivalent}\\\\\textbf{c: }(7^3)^3=7^{3\cdot3}=7^9\quad\textbf{equivalent}\\\\\textbf{d: }7^4+7^5=7^4(1+7)=8\cdot7^4\quad\textbf{not equivalent}\\\\\textbf{e: }7^4\cdot7^5=7^{4+5}=7^9\quad\textbf{equivalent}$

Answer 2

Answer:

b: 7^18 / 7^9

 c: (7^3)^3

 e: 7^4 * 7^5

Step-by-step explanation: