What is the answer to (2³)³? Explain or show your work.

Mathematics

2 answers:

Charra [1.4K]2 years ago

8 0

Answer:

(2³)³=512

because, 2³=8 & 8³=512

ipn [44]2 years ago

4 0

Answer:

512

Step-by-step explanation:

Ok, let's start by deciphering how powering works:

$a^3 = a \cdot a \cdot a\\a^b * a^c = a^{b+c}\textrm{; because it's "multiply a b times" multiplied by "multiply a c times"}\\(a^b)^c = a^{b\cdot c}\textrm{; because of the above}\\$

$(2^3)^3 = 2^{3\cdot3} = 2^9\\$

and because of KibiBytes existing, we know that 2^10 = 1024, so 2^9 will be equal to 1024/2=512

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Which of these is NOT an integer

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Hi there!

»»————-　★　————-««

I believe your answer is:

Option A

»»————-　★　————-««

Here’s why:

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$\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}$

⸻⸻⸻⸻

$\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}$

⸻⸻⸻⸻

$\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}$