Write the given number as the product of two or more powers in three different ways. The powers can be any integers. Class 8

Write the given number as the product of two or more powers in three different ways. The powers can be any integers. Class 8

Question 1.

Write the given number as the product of two or more powers in three different ways. The powers can be any integers. Class 8

(i) 64³

(ii) 192⁸

(iii) 32^-5

Solution:

(i) 64³ = (8²)³ = 8⁶; 64³ = (4³)³ = 4⁹; 64³= (2⁶)³ = 2¹⁸

(ii) 192⁸ = (4³ × 3)⁸ = 4²⁴ × 3⁸; 192⁸ = 4¹⁶ × 4⁸ × 3⁸ = 4¹⁶ × 12⁸; 192⁸ = (2⁶ × 3)⁸ = 2⁴⁸ × 3⁸.

(iii) 32^-5 = (2⁵)^-5 = 2^-25; 32^-5 = (8 × 4)^-5 = 8^-5 × 4^-5; 32^-5 = (16 × 2)^-5 = 16^-5 × 2^-5.

Question 2.

Examine each statement below and find out if it is ‘Always True’, ‘Only Some-times True’, or ‘Never True’. Explain your reasoning. Class 8

(i) Cube numbers are also square numbers.

(ii) Fourth powers are also square numbers.

(iii) The fifth power of a number is divisible by the cube of that number.

(iv) The product of two cube numbers is a cube number.

(v) q⁴⁶ is both a 4th power and a 6th power (q is a prime number).

Solution:

(i) Only sometimes true.

(ii) Always true.

(iii) Always true.

(iv) Always true.

(v) Never true.