Question

[2⁻¹ + 3⁻¹ + 4⁻¹]⁰ =__________. ​

Answer 1

Answer:

[2⁻¹ + 3⁻¹ + 4⁻¹]⁰ = 1

Step-by-step explanation:

Given,[2⁻¹ + 3⁻¹ + 4⁻¹]⁰

This is a problem of power of indices of Algebra.

By simple power of indices rule,we can solve this.

$({2}^{ - 1} + {3}^{ - 1} + {4}^{ - 1} )^ { 0} \\ = ( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} )^{0} \\ = ( \frac{6 + 4 + 3}{12} )^{0} \\ =( \frac{13}{12} )^{ 0} \\ = \frac{ {13}^{0} }{ {12}^{0} } \\ = \frac{1}{1} \\ = 1$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124 2)https://brainly.in/question/1169549

Answer 2

Answer:

The value of the expression [2⁻¹ + 3⁻¹ + 4⁻¹]⁰ is 1.

Step-by-step explanation:

Given:-

The expression is [2⁻¹ + 3⁻¹ + 4⁻¹]⁰.

To find:-

The value of the expression [2⁻¹ + 3⁻¹ + 4⁻¹]⁰.

Step 1 of 1

Consider the given expression as follows:

[2⁻¹ + 3⁻¹ + 4⁻¹]⁰

First, simplify the expression inside the square bracket as follows:

⇒ $[\frac{1}{2} + \frac{1}{3} +\frac{1}{4} ]^0$

The LCM of the numbers 2, 3 and 4 is 12.

So,

⇒ $\left[\frac{6+4+3}{12} \right]^0$

⇒ $\left[\frac{13}{12} \right]^0$ _____ (1)

As we know,

Any number raise to the power is equal to 1, i.e.,

$x^0=1$, where $x$ is any number.

Then expression (1) implies,

$\left[\frac{13}{12} \right]^0=1$

Therefore, the value of the expression [2⁻¹ + 3⁻¹ + 4⁻¹]⁰ is 1.

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