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Find an expression equivalent to the one shown below. (3⁴)5 ÷ 3⁵ OA. 3¹⁵ OB. 3⁴ OC. 3²⁵ OD. 12​

Sagot :

Amphitrite1040

Hey there!

(3^4)^(5) ÷ 3^5


3^4(5)

= 3^20

= 3,486,784,401

3^5

= 3 * 3 * 3 * 3 * 3

= 9 * 9 * 3

= 81 * 3

= 243


= 3,486,784,401 ÷ 243

= 14,348,907



SIMPLIFY IT!

= 14,348,907

≈ 3^15


Therefore, your answer is: 3^15


Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Explanation:

Let's review three examples of product of exponent rule and dividing of exponent rule before solving the problem.

  • (a²)³ = a²⁽³⁾ = a⁶
  • {[(b³)⁵}⁷] = b³⁽⁵⁾⁽⁷⁾ = b¹⁰⁵
  • (a²) ÷ a = a²⁻¹ = a

Looking at these examples, we can tell that we can multiply exponents and subtract exponents. These rules are applied in this question. Now, let's solve the question to obtain our answer.

Solution:

  • (3⁴)⁵ ÷ 3⁵
  • => 3⁴⁽⁵⁾ ÷ 3⁵
  • => 3²⁰ ÷ 3⁵
  • => 3²⁰⁻⁵
  • => 3¹⁵

Final Answer:

  • 3¹⁵ or Option A
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