Question

Choose the expressions that are perfect cubes.

Answer 1

Answer with explanation:

⇒A number is a perfect cube , if we multiply a number thrice to itself ,and then that number obtained is said to be perfect cubic number.

→a×a×a=a³

Here,a³ is a perfect cubic number,and a is said to be cube root of a³(that is perfect cubic number).

→A: -3 ⇒ No number when multiplied ,thrice gives -3.So, -3 is not a perfect cube.

→$B:125 a^6=5 a^2\times 5 a^2 \times 5 a^2\\\\(125 a^6)^{\frac{1}{3}}=5 a^2$

This number is a perfect cube.

→$C: (8 m^{20})^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}*(m^{20})^{\frac{1}{3}}=2*m^{\frac{20}{3}}$

Not, a Perfect cube.

→$D: (100*w^{24}*x^3)^{\frac{1}{3}}=(10^2)^{\frac{1}{3}}*(w^{24})^{\frac{1}{3}}*(x^3)^{\frac{1}{3}}\\\\=10^{\frac{2}{3}}*w^8*x$

Not, a Perfect cube

$E:(-64*q^{12})^{\frac{1}{3}}=[(-4)]^{3\times\frac{1}{3}}*(q^{12})^{\frac{1}{3}}\\\\=-4*q^4\\\\F:[c^{30}*d^9*f^{18}*g^3]^{\frac{1}{3}}\\\\=[c^{30}]^{\frac{1}{3}}*(d^9)^{\frac{1}{3}}*(f^{18})^{\frac{1}{3}}*(g^3)^{\frac{1}{3}}\\\\=c^{10}*d^3*f^6*g$

E and F are Perfect cubes.

Keep the following law of indices in mind

$1.(a^m)^n=a^{mn}\\\\2.(a^m){\frac{1}{n}}=a^{\frac{m}{n}}\\\\3.a*a*a=a^3\\\\4.a^{3 m*{\frac{1}{3}}}=a^m$

Option : B, E and F are perfect cubes.

Answer 2

Its 2,5,6 on edenuity