Question

If $7^{10}=7\times 7^n$, what is the value of $n$?

• A. $10$
• B. $9$
• C. $7$
• D. $5$
• E. $3$

Answer 1

Answer: (B)

$9$

Given, $7^{10}=7^1\times 7^n$

$\Rightarrow 7^{10}=7^{1+n}[\because x^a\times x^b=x^{a+b}]$

$\Rightarrow 10=1+n$ [Since bases are equal, their powers must be equal]

$\Rightarrow n=10-1$
$\Rightarrow n=9$