Question

Which of the following is equal to x^3?

65 points

a. x^6 – x^3

b. x^6.x^3

c. x^6/x^3

d. (x^6)^3​

Answer 1

Answer:

$\longrightarrow$ c). $\Large\frac{ {x}^{6} }{ {x}^{3} }$

Step-by-step explanation:

$\Huge\mathcal{\green{Question:-}}$

$\hookrightarrow$ Which of the following is equal to ${x}^{3}$?

$\:$ a). $\:$ ${x}^{6}$ - ${x}^{3}$

$\:$ b). $\:$ ${x}^{6}$ $\times$${x}^{3}$

$\:$ c). $\:$ $\Large\frac{ {x}^{6} }{ {x}^{3} }$

$\:$ d). $\:$ ${ ({x}^{6}) }^{3}$

$\Huge\mathtt{\purple{Hint:-}}$

• We will use the concept of laws of Exponents.

$\Huge\mathfrak{\red{Solution:-}}$

Let's check for all the given options:-

$\:$ a). $\:$ ${x}^{6}$ - ${x}^{3}$

Since, there is no specific law of Exponents related to this. So, this option is not correct.

$\:$ b). $\:$ ${x}^{6}$ $\times$ ${x}^{3}$

We know that, ${a}^{m}$ $\times$ ${a}^{n}$ = ${a}^{m + n}$

$\therefore$ $\:$ ${x}^{6}$ $\times$ ${x}^{3}$ = ${x}^{6 + 3}$ = ${x}^{9}$

So, this option is also not correct.

$\:$ c). $\:$ $\Large\frac{ {x}^{6} }{ {x}^{3} }$

We know that, $\Large\frac{ {a}^{m} }{ {a}^{n} }$ = ${a}^{m - n}$

$\therefore$ $\:$ $\Large\frac{ {x}^{6} }{ {x}^{3} }$ = ${x}^{6 - 3}$ = ${x}^{3}$

$\:$ d). $\:$ ${ ({x}^{6}) }^{3}$

We know that, ${ ({a}^{m}) }^{n}$ = ${a}^{m × n}$

$\therefore$ $\:$ ${ ({x}^{6}) }^{3}$ = ${x}^{6 × 3}$ = ${x}^{18}$

So, this is also not correct.

Hence, option (c) is the correct option.