Question

Find the cube root of the following numbers:

(i)-216 x 3375

(iii) -27/4096.

5. Evaluate:

(ii) 729x 2197

(iv) -2197/-9261​

Answer 1

Step-by-step explanation:

(i)-216 x 3375

³√-216 x 3375 = - ³√(6/15)³

= - 6/15 ^(3×1/3)

= - (6/15)¹

= 2/5

iii) -27/4096.

³✓ -27/4096 = -³√(27/4096)

= ³√3³/2¹²

=[ 3^(3×1/3) ] / 2^(12/3)

= 3¹/2⁴

= 3/(2x2x2x2)

= 3/16

ii) 729x 2197

³√ 729x 2197 = ³√ (3⁶/13³)

=[ 3^(6/3) ] / (13 ^ (3×1/3))

= 3² / 13

= 9/13

(iv) -2197/-9261

³√-2197/-9261 = ³√ 2197/9261

= ³√ (13³/(7×3)³)

= ³√(13³/21³)

= 13/21