Question

Which of the following is equal to x3?

Answer 1

Answer:

Step-by-step explanation:

x^6/x^3=x^6-3=x^3

because power in divide got subtracted

Answer 2

Question: Which of the following is equal to $x^3$ ?

(i) x⁶ - x³     (ii) x⁶.x³       (iii) x⁶ / x³       (iv) x⁶ / 2

Answer:

Option (iii) is the correct answer.

Step-by-step explanation:

Recall the law of exponents,

$x^ax^b=x^{a+b}$

$\frac{x^a}{x^b} =x^{a-b}$

$(x^a)^b=x^{ab}$

(i) $x^6-x^3$

Simplify as follows:

⇒ $x^3x^3-x^3$ (Using $x^ax^b=x^{a+b}$)

⇒ $x^3(x^3-1)$

⇒ $x^3(x^3-1)\neq x^3$

Thus, option (i) is not correct.

(ii) $x^6x^3$

Simplify as follows:

⇒ $x^{6+3}$ (Using $x^ax^b=x^{a+b}$)

⇒ $x^9$

⇒ $x^9\neq x^3$

Thus, option (ii) is not correct.

(iii) $x^6/x^3$

Simplify as follows:

⇒ $x^{6-3}$ (Using $\frac{x^a}{x^b} =x^{a-b}$)

⇒ $x^3$

⇒ $x^3\neq x^3$

Thus, option (iii) is correct.

(iv) $x^6/2$

Simplify as follows:

⇒ $\frac{1}{2} x^6$

⇒ $\frac{1}{2} x^6\neq x^3$

Thus, option (iv) is not correct.

Therefore, the expression $x^6/x^3$ is equal to $x^3$.

#SPJ3