CBSE Class 9 Maths solutions Number Systems Ex 1.6 | Operations on Real nimbers

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00:02 Q1. Find :

00:28 (i) 64^(1/2)

01:02 Power of a power

If we take the power of a product, then result is a single exponential where the power is the product of the original exponents.

01:32 (ii)32^(1/5)

01:45 Factor tree of 32

02:34 Apply law of rational exponent Power of a power

03:15 (iii)125^(1/3)

03:30 factorization of 125

04:03 Power of a power: When raising a power to a power, multiply the exponents.

04:35 Q2. Find :

05:04 (i) 9^(3/2)

05:39 USE LAW OF EXPONENT:Power of a power

06:23 (ii) 32^(2/5)

08:00 (iii) 16^(3/4)

09:22 (iv) 125^(-1/3)

10:09 Apply law of rational exponent Power of a power

If we take the power of a product, then result is a single exponential where the power is the product of the original exponents.

10:35 changing sign of exponent

This Law of exponent states changing the sign of a exponent gives the reciprocal.

10:56 Q3. Simplify :

11:36 (i)2^(2/3) * 2^(1/5)

11:45 Product of exponentials with same base

This law of exponent states if we take the product of two exponentials with the same base, we simply add the exponents.

12:26 Addition of fractions 2/3 and 1/5.

13:46 (ii) (1 / (3^3))^7

14:10 Quotient of exponentials with same base

This law of exponent states if we take the quotient of two exponentials with the same base, we simply subtract the exponents.+

15:03 Apply law of exponent:Power of power

15:37 Apply law of exponent:changing sign of exponent

changing the sign of a exponent gives the reciprocal.

15:55 (iii) 11^(1/2) / 11^(1/4)

16:13 Apply law of exponent : Quotient of exponentials with same base

If we take the quotient of two exponentials with the same base, we simply subtract the exponents.

16:33 Subtraction of fractions.

17:56 (iv) 7^(1/2) * 8^(1/2)

18:12 Apply law of exponent : Power of a product

If we distribute the exponent over the different factors, we take the power of a product.

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