Laws of Exponents

If $y={\left(\frac{4}{9}\right)}^3÷{\left(\frac{2}{3}\right)}^4\times \left(\frac{3}{4}\right)$, then find the value of $y+2$.

If ${\left(\frac{3}{5}\right)}^4=a, {\left(\frac{-5}{3}\right)}^0=b$, if the value of ${\left(\frac{a}{b}\right)}^4$ is ${\left(\frac{3}{5}\right)}^k$.

Then find the value of $k$.

If the value of ${\left(10\right)}^{100}\times {\left(-100\right)}^{10}={100}^k$.

Then find the value of $k$.

On simplification if ${\left[{\left(3^2\right)}^4\times 3^4\right]}^2÷{\left(3^8\right)}^2=3^k$.

Then find the value of $k$.

Simplify: ${\left[{\left\{{\left(-5\right)}^2\right\}}^0\right]}^2$

Simplify: $\left\{4^0÷4^1\right\}\times 4$

Simplify: ${\left[{\left(\frac{-3}{5}\right)}^2\right]}^3$

Simplify: ${\left(3-1\right)}^0$

Simplify: ${\left(-4\right)}^5÷{\left(4\right)}^4$

Simplify: ${\left(7^2\right)}^3÷7^3$

Simplify: $\left(\frac{5^5}{5^3}\right)\times 5^2$

Find the value of $x$, if ${\left(2\right)}^{x+1}\times 2={\left(2\right)}^{12}÷{\left(2\right)}^3$.

Take any two $5$-digit numbers and express them in the standard form, in the binary number system and also in the hexadecimal number system.

Verify all the laws of exponents by choosing some small whole numbers for $a, b, m$ and $n$.

Simplify:

${\left(\frac{1}{2}\right)}^4÷{\left(\frac{{\displaystyle 1}}{{\displaystyle 2}}\right)}^4$

Simplify: ${\left(-10\right)}^9÷{\left(-10\right)}^9$

Simplify: $d^3÷d^3$

Complete the following table:

Complete the following table:

Complete the following table.