Exponents Challenge

Algebra Level 2

$\Large 3^{3^3} \div 3^3 = \ ?$

3^{3}

3^9

3^{26}

3^{24}

3 solutions

Pulkit Gupta
Dec 15, 2015

The answer is $\Large3^{24}$

To those who need explanation : $\Large 3^{3^3} \div 3^3$ $\Large=$ $\Large 3^{27} \div 3^3$ $\Large=$ $\Large 3^{24}$

This rule is known as the Tower Rule of exponents. Read more here : Simplify Exponents

Its a common misconception in exponents to treat $(3^{3})^{3}$ & $\ 3^{3^3}$ as similar. While the former evaluates to $3^{9}$ , the latter evaluates to $3^{27}$ .

answer = 3^24 all day, yes.

Michael Mello - 5 years, 5 months ago

Yes. I think so.!!!

Prasit Sarapee - 5 years, 6 months ago

Thanks. I have updated the answer to $3^{24}$ .

Calvin Lin Staff - 5 years, 5 months ago

no ....answer would be 3^6

Ramesh Kumar - 5 years, 6 months ago

That's a common misconception.

Refer the tower rule here : https://brilliant.org/wiki/simplify-exponents/

Pulkit Gupta - 5 years, 6 months ago

Did you think that $3^{3} = 9$ ?

Evan Huynh - 5 years, 5 months ago

Ya you r right the ans is 3^6 but there is no option.

Yasir Javed - 5 years, 5 months ago

Sarnodeep Agarwalla
Dec 17, 2015

The Ans should be 3^24

3^3^3=3^27

3^27/3^3 =3^(27-3) =3^24

Thanks. I have updated the answer to $3^{24}$ .

Calvin Lin Staff - 5 years, 5 months ago

Gareth Adamson
Dec 17, 2015

According to exponent rules, when two powers with the same base are divided, you subtract the exponents.

3 ^ (3^3) / 3^3 = x

3 ^ 3 = 27

3 ^ 27 / 3 ^ 3 = x

3 ^ (27 - 3) = x

3 ^ 24 = x

Exponents Challenge

3 solutions

To those who need explanation : 3 3 3 ÷ 3 3 \Large 3^{3^3} \div 3^3 3 3 3 ÷ 3 3 = \Large= = 3 27 ÷ 3 3 \Large 3^{27} \div 3^3 3 2 7 ÷ 3 3 = \Large= = 3 24 \Large 3^{24} 3 2 4

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To those who need explanation : $\Large 3^{3^3} \div 3^3$ $\Large=$ $\Large 3^{27} \div 3^3$ $\Large=$ $\Large 3^{24}$