Rahul Sofat Solutions for Chapter: Exponents and Powers, Exercise 5: EXERCISE 5.2

Simplify each of the following and express each as a rational number:

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{3}{5}\right)}^4\times {\left(\frac{7}{2}\right)}^3$

Simplify each of the following and express each as a rational number:

${\left(\frac{-1}{3}\right)}^5\times 3^3\times {\left(\frac{3}{4}\right)}^2$

Simplify each of the following and express each as a rational number:

$\left\{{\left(\frac{-3}{4}\right)}^3÷{\left(\frac{-5}{2}\right)}^3\right\}÷2^3$

Simplify $\left\{{\left(\frac{3}{17}\right)}^{11}\times {\left(\frac{{\displaystyle 3}}{{\displaystyle 17}}\right)}^7\right\}÷\left\{{\left(\frac{{\displaystyle 3}}{{\displaystyle 17}}\right)}^8\times {\left(\frac{{\displaystyle 3}}{{\displaystyle 17}}\right)}^{10}\right\}$ and express the result as power of $10$.

Determine the value of $x$ in each of the fallowing:

${\left\{{\left(3\right)}^3\right\}}^7=3^{7x}$

Determine the value of $x$ in each of the fallowing:

${\left(-2\right)}^{11}÷{\left(-2\right)}^9={\left(-2\right)}^{2x}$

Determine the value of $x$ in each of the fallowing:

${\left(47\right)}^x÷{\left(47\right)}^{21}={\left(47\right)}^{45}$

Determine the value of $x$ in each of the fallowing:

${\left(\frac{2}{3}\right)}^{26}÷{\left(\frac{2}{3}\right)}^{22}={\left(\frac{2}{3}\right)}^3$