Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

General

General

Easy

Question

Simplify the following
$open parentheses left parenthesis 2 divided by 3 right parenthesis squared close parentheses cubed cross times left parenthesis 1 divided by 3 right parenthesis to the power of negative 2 end exponent cross times 3 to the power of negative 1 end exponent cross times 1 divided by 64$

hint Hint:

In Mathematics, lets say, "a" represents a number and " " is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
$a to the power of n equals a cross times a cross times horizontal ellipsis cross times a$ n times.

The correct answer is: 1/243

Hint:-
In Mathematics, lets say, "a" represents a number and " " is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as aⁿ, where a is called the base and n is its power/ exponent.
$a to the power of n equals a cross times a cross times horizontal ellipsis cross times a$ n times.
$open parentheses left parenthesis 2 divided by 3 right parenthesis squared close parentheses cubed cross times left parenthesis 1 divided by 3 right parenthesis to the power of negative 2 end exponent cross times 3 to the power of negative 1 end exponent cross times 1 divided by 64$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank row cell equals left parenthesis 2 divided by 3 right parenthesis to the power of 2 cross times 3 end exponent cross times left parenthesis 1 divided by 3 right parenthesis to the power of negative 2 end exponent cross times 3 to the power of negative 1 end exponent cross times 1 divided by 64 horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis. horizontal ellipsis open square brackets open parentheses b to the power of n close parentheses to the power of m equals b to the power of n m end exponent close square brackets end cell end table$
$table attributes columnalign right columnspacing 0em end attributes row cell equals left parenthesis 2 divided by 3 right parenthesis to the power of 6 cross times left parenthesis 3 divided by 1 right parenthesis squared cross times left parenthesis 1 divided by 3 right parenthesis to the power of 1 cross times 1 divided by 64 end cell row blank row blank row blank end table$ $open parentheses b to the power of negative n end exponent equals 1 divided by b to the power of n close parentheses$
$equals 2 to the power of 6 divided by 3 to the power of 6 cross times left parenthesis 3 right parenthesis squared cross times 1 divided by 3 to the power of cross times 1 divided by 64$ $open square brackets a to the power of n divided by b to the power of n equals left parenthesis a divided by b right parenthesis to the power of n straight & b to the power of 1 equals b close square brackets$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 64 divided by 729 cross times 9 cross times 1 divided by 3 cross times 1 divided by 64 end cell row blank row blank end table$
$table attributes columnalign right columnspacing 0em end attributes row cell equals 576 divided by 139968 end cell row blank end table$
$equals 1 divided by 243$
Final Answer:-
Simplifying the given expression, we get the answer:- 1/243

Related Questions to study

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.