Question

CLASS 7 MATHS

CH-13- EXPONENTS AND POWERS

FIND THE RECIPROCAL OF
A) $(-2/3)^{4}$
B) $(-2/3)^{3}$ × $(3/4)^{4}$

Answer 1

A ) : ( - 2 / 3 )⁴


From the properties of exponents and powers, we know :

Any negative number with an even number in its power is equal to the sfame number with positive sign ( instead of negative ).

Therefore,

= > ( - 2 / 3 )^4

= > ( 2 / 3 )^4

= > ( 2 x 2 x 2 x 2 ) / ( 3 x 3 x 3 x 3 )

= > 16 / 81


Then, reciprocal of 16 / 81 = 81 / 16


Hence,
Reciprocal of ( - 2 / 3 )^4 is 81 / 16.




B ) : ( - 2 / 3 )^3 + ( 3 / 4 ).

From the properties of exponents and powers, we know :

Any negative number with an even number in its power is equal to the sfame number with positive sign ( instead of negative ).

But in this case, ( - 2 / 3 )^3 is with a negative number in its power. So, ( - 2 / 3 )^3 will ( - 2 / 3 )^3 only.


= > ( - 2 / 3 )^3 x ( 3 / 4 )^4
.

= > [ ( - 2 x - 2 x - 2 ) / ( 3 x 3 x 3 ) ] x [ ( 3 x 3 x 3 x 3 ) / ( 4 x 4 x 4 x 4 )


= > - 3 / 32


Hence,
Reciprocal of ( - 3 / 32 ) is - 32 / 3.
$\:$

Answer 2

Answer :

A) 81 / 16

B) -32 / 3

Step-by-step explanation :

Given :

A) ( - 2 / 3 )⁴

Using the law of exponents and powers, we know that, if there is a negative number and have a even number as power, then the negative number is also written positively.

Here,

( - 2 / 3 )⁴ can be written as ( 2 / 3 )⁴

On simplifying it, we get ;

( 2 / 3 )⁴

⇒ ( 2 × 2 × 2 × 2 ) / ( 3 × 3 × 3 × 3 )

⇒ 16 / 81

The reciprocal of 16 / 81 is 81 / 16.

Hence, the reciprocal of ( - 2 / 3 )⁴ will be 81/16.

_______________________

B) ( - 2 / 3 )³ × ( 3 / 4 )⁴

Here, the power of negative number is not even, i.e., odd. Therefore, the sign will not change.

On Simplifying, we have ;

( - 2 / 3 )³ × ( 3 / 4 )⁴

⇒ [{(-2) × (-2) × (-2)} / ( 3 × 3 × 3 )] × ( 3⁴ / 4⁴ )

⇒ - 8 / 27 × 81 / 256

⇒ - 648 / 6912

⇒ - 72 / 768

⇒ - 24 / 256

⇒ - 3 / 32

Hence, the reciprocal of - 1 / 32 is - 32 / 3.