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

Evaluate the following: ${\left[{\left(\frac{5}{4}\right)}^{-2}÷{\left(\frac{1}{2}\right)}^{-3}\right]}^{-1}$

Simplify:

${\left(2^{-1}÷3^{-1}\right)}^3\times {\left(-\frac{9}{4}\right)}^{-2}$

If $\left(\frac{p}{q}\right)={\left(\frac{3}{7}\right)}^{-2}\times {\left(\frac{2}{7}\right)}^0$, then find ${\left(\frac{p}{q}\right)}^{-1}$.

If the base of a triangle is ${\left(\frac{5}{3}\right)}^3\mathrm{m}$ and its altitude is ${\left(\frac{9}{2}\right)}^2\mathrm{m}$, find the area of triangle.

Verify the following: ${\left[{\left(\frac{2}{3}\right)}^{-1}+\frac{1}{2}-{\left(\frac{3}{4}\right)}^2\right]}^{-1}=\frac{16}{23}$.

Find the value of $\frac{{\left(4\right)}^{-3}\times t^5\times 45}{{\left(t\right)}^3\times {\left(4\right)}^{-5}\times {\left(15\right)}^2}$.

Find the value of $x^2$, if

${\left(\frac{5}{9}\right)}^{-3}\times {\left(\frac{25}{81}\right)}^{-3x}={\left(\frac{9}{5}\right)}^{2x+5}$

Evaluate: ${\left[{\left(1^2+2^2+3^2+4^2\right)}^{-1}\right]}^1$