Jharne De and Ranjana Kumar Solutions for Chapter: Exponents (Powers), Exercise 6: Test Paper 2

If $2^3\times 2^5\times 2^7=2^k$, then $k=$ _____.

Express in power notation: $\frac{-343}{ 512}$

Solve: $\left[\right({5^{-2})}^5\times 5^{15}]÷5^{-28}$

What number will divide $3^{-2}$to get $9^2$?

Find the value of $a$ if ${\left(\frac{3}{5}\right)}^{3a}\times {\left(\frac{3}{5}\right)}^{4a+3}={\left(\frac{3}{5}\right)}^{52}$

Find the value of $b$ if ${\left(\frac{2}{5}\right)}^{7-b}\times {\left(\frac{5}{2}\right)}^{2+4b}={\left(\frac{2}{5}\right)}^{3b-5}$

If $\left(\frac{x}{y}\right)=\frac{3}{7}$, then find the value of ${\left(\frac{x^2}{y^2}\right)}^{-2}$

Simplify: $\frac{2^3\times 3^{-1}\times 4^2}{3^{-2}\times 2^{-1}\times 4^3}$