Explanation

The notation n√x^m can be rewritten in power form as:

(x^m)^(1/n) = x^(m/n)

Explanation

Explanation

Given the expression:

[(2/13)⁶ + (2/13)³]³ × (2/13)^-⁹

Let's simplify:

= [(2/13)³((2/13)³ + 1)]³ × (2/13)^-⁹

= (2/13)⁹[(2/13)³ + 1]³ × (2/13)^-⁹

The (2/13)⁹ and (2/13)^-⁹ cancel out:

= [(2/13)³ + 1]³

Given the result is 1, let's assume:

[(2/13)³ + 1]³ = 1

Explanation

Substitute the given values:

a = 1, b = 0, c = -1

Now, evaluate the expression:

(a - c) - (a + b) + ab

= (1 - (-1)) - (1 + 0) + 1(0)

= (1 + 1) - 1 + 0

= 2 - 1

= 1

Explanation

Loga (m × n) = Loga m + Loga n.

This is a logarithmic property: the log of a product is the sum of the logs.

Explanation

4x + 13 = 7 - 2x

Add 2x to both sides:

4x + 2x + 13 = 7

Combine like terms:

6x + 13 = 7

Subtract 13 from both sides:

6x = -6

Divide both sides by 6:

x = -6/6

x = -1

Explanation

x²y and xy² have the same variables but with different exponents, so they are not like terms.

Unlike terms cannot be combined through addition or subtraction.

Explanation

Given x + 1/x = 10:

Step 1: Square both sides

(x + 1/x)² = 10²

x² + 2(x)(1/x) + 1/x² = 100

x² + 2 + 1/x² = 100

Step 2: Solve for x² + 1/x²

x² + 1/x² = 100 - 2

x² + 1/x² = 98

Explanation

Given cosx(tan x + cot x):

Step 1: Express tan x and cot x in terms of sin x and cos x

tan x = sin x / cos x

cot x = cos x / sin x

Step 2: Substitute and simplify

cosx(tan x + cot x) = cosx(sin x / cos x + cos x / sin x)

= sin x + cos² x / sin x

= (sin² x + cos² x) / sin x

= 1 / sin x (since sin² x + cos² x = 1)

Step 3: Identify the result

1 / sin x = cosec x

Explanation

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