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

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.