S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 2: Check Point

Find the value of $p$ in the following:

${\left[{\left(\frac{7}{3}\right)}^5\right]}^2={\left(\frac{7}{3}\right)}^{p+3}$

Simplify:

$2^{55}\times 2^{60}-2^{97}\times 2^{18}$

Simplify:

$\frac{3^n+3^{n+1}}{3^{n+1}-3^n}$

Simplify:

$\frac{10\times 5^{n+1}+25\times 5^n}{3\times 5^{n+2}+10\times 5^{n+1}}$

Find the value of $x$ in the following:

$2^{x-7}\times 5^{x-6}=50$

Find the value of $x$ in the following:

$5^{x-3}\times 3^{2x-8}=225$

Find the value of $x$ in the following:

${25}^{x-1}=5^{2x-1}$

Find the value of $x$ in the following:

$2^{x-5}\times 5^{x-4}=5$