(-4)⁻⁴ × (4)⁻¹ = (4)⁵. State whether the statement is true or false.

Solution:

Given, (-4)⁻⁴ × (4)⁻¹ = (4)⁵

The given expression can be rewritten as (-4)⁻⁴ = (4)⁵/(4)⁻¹

Using law of exponents,

a⁻ⁿ = 1/aⁿ

So, (4)⁻¹ = 1/4

Similarly, (-4)⁻⁴ = 1/(-4)⁴

LHS: (-4)⁻⁴

= 1/(-4)⁴

RHS: (4)⁵/(4)⁻¹

= (4)⁵/(1/4)

= (4)⁵ × 4

Using the law of exponents,

a^m × aⁿ = a^{m + n}

= 4^{5 + 1}

= 4⁶

LHS ≠ RHS

✦ Try This: (-3)⁻¹ × (-3)⁻⁵ = (3)⁵. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 72

(-4)⁻⁴ × (4)⁻¹ = (4)⁵. State whether the statement is true or false.

Summary:

The given statement, ”(-4)⁻⁴ × (4)⁻¹ = (4)⁵” is false using the laws of exponents.

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☛ Related Questions:

• (2/3)⁻² × (2/3)⁻⁵ = (2/3)¹⁰. State whether the statement is true or false
• 5⁰ = 5. State whether the statement is true or false
• (-2)⁰ = 2. State whether the statement is true or false