Question

If ${\left(\frac{x^m\times x^n}{x^p}\right)}^q=x^K$ then what is the value of K?

• A. (pq) (mn)
• B. (m + n - p)q
• C. (m + n + q)
• D. (m + n) (n + q)

Answer 1

The correct option is B (m + n - p)q

${\left(\frac{x^m\times x^n}{x^p}\right)}^q=x^K$

$\Rightarrow {\left(\frac{x^{m+n}}{x^p}\right)}^q=x^K[\because a^m\times a^n=a^{m+n}]$

$\Rightarrow (x^{m+n-p}{)}^q=x^K[\because a^m÷a^n=a^{m-n}]$

$\Rightarrow x^{(m+n-p)q}=x^K[\because (a^m{)}^n=a^{mn}]$

$\Rightarrow K=(m+n-p)q$