Find the multiplicative inverse of (-7)⁻² ÷ (90)⁻¹.
Solution:
Given, the expression is (-7)⁻² ÷ (90)⁻¹.
We have to find the multiplicative inverse.
Using law of exponents,
a⁻ⁿ = 1/aⁿ
So, (-7)⁻² = 1/(-7)⁻²
= (-7)²
= 49
Similarly, (90)⁻¹ = 1/(90)⁻¹
= 90
Now, (-7)⁻² ÷ (90)⁻¹ = (1/49) ÷ (1/90)
= 90/49
The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1.
i.e., a × b = 1
Let b = 90/49
So, a × (90/49) = 1
a = 1/(90/49)
= 49/90
Therefore, the multiplicative inverse is 49/90.
✦ Try This: Find the multiplicative inverse of (-5)⁻³ ÷ (99)⁻¹
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 104
Find the multiplicative inverse of (-7)⁻² ÷ (90)⁻¹.
Summary:
The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1. The multiplicative inverse of (-7)⁻² ÷ (90)⁻¹ is 49/90.
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