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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Simplify: [(1/2)² - (1/4)³]⁻¹ × 2⁻³.
Solution:
Given, the expression is [(1/2)² - (1/4)³]⁻¹ × 2⁻³.
We have to simplify the expression.
Considering [(1/2)² - (1/4)³]⁻¹,
(1/2)² = 1/4
(1/4)³ = 1/64
[(1/2)² - (1/4)³]⁻¹ = [1/4 - 1/64]⁻¹
= [(16 - 1)/64]⁻¹
= (15/64)⁻¹
Using the law of exponents,
a⁻ⁿ = 1/aⁿ
(15/64)⁻¹ = 1/(15/64)
= 64/15
Similarly, 2⁻³ = 1/2³
= 1/8
Now, [(1/2)² - (1/4)³]⁻¹ × 2⁻³ = (64/15) × 1/8
= 8/15
Therefore, the simplified value is 8/15.
✦ Try This: Simplify: [(1/3)² - (1/2)³]⁻¹ × 3⁻³.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 180(1)
Simplify: [(1/2)² - (1/4)³]⁻¹ × 2⁻³
Summary:
The simplified value of [(1/2)² - (1/4)³]⁻¹ × 2⁻³ is 8/15 using the law of exponents a⁻ⁿ = 1/aⁿ
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