A Three For You And A Three For Me

Algebra Level 1

( 3 × 3 3 ) 3 × ( 33 ) 3 \large \left( 3 \times 3^3\right)^3 \times (33)^3

Evaluate the expression above.

( 33 × 33 ) 3 ( 33 \times 33)^3 ( 27 × 33 ) 3 (27 \times 33)^3 ( 81 × 33 ) 3 (81 \times 33)^3 ( 333 × 3 ) 3 ( 333 \times 3)^3

View wiki
Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Rishabh Jain
Feb 19, 2016

By rules of exponents , a b × a c = a b + c a^b \times a^c = a^{b+c} .

( 3 × 3 3 ) 3 × ( 33 ) 3 = ( 3 × 3 3 × 33 ) 3 = ( 3 × 27 × 33 ) 3 = ( 81 × 33 ) 3 \large \begin{aligned} ( 3 \times 3^3)^3 \times (33)^3 &=&( 3 \times 3^3 \times 33)^3 \\ &=&(3\times 27 \times 33)^3 \\ &=&(81 \times 33)^3 \end{aligned}

15 Helpful 0 Interesting 0 Brilliant 0 Confused

Quite Quick! Thanks :)

Sandeep Bhardwaj - 5 years, 3 months ago

What? Not fair. I submitted my solution first :3

Mehul Arora - 5 years, 3 months ago

Log in to reply

Yeah.. :).. Both have submitted almost at the same time.. (the difference is in seconds .. Quite competitive.. ;-)

Rishabh Jain - 5 years, 3 months ago

Log in to reply

Yeah true :P

Mehul Arora - 5 years, 3 months ago
Mehul Arora
Feb 19, 2016

( 3 × 3 3 ) 3 × 3 3 3 = ( 3 × 27 ) 3 × 3 3 3 = ( 81 × 33 ) 3 □ \large ({3 \times 3^3)^3 \times 33^3 = (3 \times 27)^3 \times 33^3 = (81 \times 33)^3} _\square

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Quite Quick! Thanks :)

Sandeep Bhardwaj - 5 years, 3 months ago
Anne Beatriz
Feb 26, 2016

Given the Property a m ⋅ b m = ( a ⋅ b ) m a^m\cdot b^m=(a\cdot b)^m , get: ( 3 ⋅ 3 3 ) 3 ⋅ ( 33 ) 3 = (3\cdot3^3)^3 \cdot (33)^3= ( 3 4 ⋅ 33 ) 3 (3^4\cdot33)^3 = ( 81 ⋅ 33 ) 3 . =(81\cdot33)^3.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...