Question

State the Laws of Indices for rational exponents.
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Answer 1

Answer:

x^m * x^n = x^m+n

x^m / x^n = x^m-n

(x^m)^n = x^mn

b√(xa) = xa/b

Step-by-step explanation:

Answer 2

The laws of indices for the rational exponents are given below –

★ If x is any rational number and a,b are rational exponents then x^a × x^b = x^a+b.

★ If x be any rational number (x > 0), a and b are rational exponents then x^a ÷ x^b = x^a-b.

★ If x (x > 0) is a rational number and a, b are rational exponent, then the expression for this law will be (x^a)^b = x^ab = (x^b)a.

★ If x,y > 0 a rational number and a is rational exponent, then x^a × x^b = (xy)^a.

★ If x, y > 0 are rational number, where y≠0 and a is a rational exponent, then the expression for this law will be

$\binom{x}{y}^{2} = \frac{ {x}^{a} }{ {y}^{a} }$

Now let us see some basic of this chapter exponent and radicals –

Zero exponent –

• [ for any Non-zero rational number]
• [ Number a, we define a° = 1]

Negative integral exponent –

• [ Let a be any non zero rational number]
• [ and n be a positive integer, then we define

– a-^n = 1/a^n