Exponents

The population of a bacteria grows according to the following equation $p=1.25\times {10}^{x+2}$, where $p$ is the population and $x$ is the number of hours.

What is the population of bacteria, in millions, after $7$ hours?

State whether the following statement is true or false.

The number of moves required in the Tower of Hanoi problem for $k$ disks can be expressed as $2^k-1$.

What is the number of moves required in the Tower of Hanoi problem for $k$ disks?

Given nano (prefix) in expanded form : $\frac{1}{1000000000}$. Express it in exponential form.

Simplify $20a^7÷10a^4$

In the following relation find the value of $x$. 

Solve the following. Write your answer as a simplified fraction.

${\left(64\right)}^{\frac{1}{3}}$

 If $x=2$ is a solution of the equation $\frac{4(x+1)}{3}-\frac{3x}{2}=\frac{5k+2}{7}$, find the value of $K$.

Evaluate : $\frac{2^{m+1}\times 3^{2m-n}\times 5^{m+n}\times 6^n}{6^m\times {10}^{n+2}\times {15}^m}$

Solve for $x$ : $2^3(5^0+3^{2x})=8\frac{8}{27}$.

Solve for x : ${\left(\sqrt[3]{4}\right)}^{2x+\frac{1}{2}}=\frac{1}{32}$

Find the value of $x$ if $\sqrt{{\left(\frac{3}{5}\right)}^{1-2x}}=4\frac{17}{27}$.

Solve the equation : ${\left(\sqrt{\frac{3}{5}}\right)}^{x+1}=\frac{125}{27}$

Evaluate : ${\left(81\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}-{\left(\frac{1}{32}\right)}^{-\frac{2}{5}}+{\left(8\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(\frac{1}{2}\right)}^{-2}{\left(2\right)}^0$

Evaluate : $9^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2 $}\right.} -3\times 5^0-{\left(\frac{1}{81}\right)}^{-\frac{1}{2}}$

Evaluate : ${\left(\frac{64}{125}\right)}^{\raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}÷\frac{1}{{\displaystyle {\left(\frac{256}{625}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}}+{\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)}^0$

Evaluate : $5^0\times 4^{-1}+8^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$.

Solve for $x$ : $\sqrt{\left(8^0+\frac{2}{3}\right)}= (0.6{)}^{2-3x}$.

Solve the equation :

$3\left(2^x+1\right)-2^{x+2}+5=0$

Evaluate: $\frac{5^{2n+3}-(25{)}^{n+2}}{{\displaystyle {\left[{\left(125\right)}^{n+1}\right]}^{\frac{2}{3}}}}$