Question

$x$ is a non-zero rational number. Product of the square of $x$ with the cube of $x$ is equal to the

• A. second power of $x$
• B. third power of $x$
• C. fifth power of $x$
• D. sixth power of $x$

Answer 1

The correct option is C

fifth power of $x$

Explanation for the correct option.

It is given that

The square of $x=x^2$

The cube of $x=x^3$

Product of $x^2$ and $x^3$ is,

$$\begin{gathered} x^2\times x^3=x^{2+3} \\ \Rightarrow x^2\times x^3=x^5\left[\because x^a\times x^b=x^{a+b}\right] \\ \therefore x^2\times x^3=x^5 \end{gathered}$$

Product is the fifth power of $x$.

Hence, option $\left(\mathrm{C}\right)$ is correct.