Basics of Exponents and Powers

If $2^3+2^x=2^4$, then $x$ equals 

Calculate the value of $9^2$.

Calculate the value of $3^2$

If $\left(3.769\times {10}^5\right)+\left(4.21\times {10}^5\right)=k\times {10}^5$.

Then find the value of $k$.

Find the value of $(-3{)}^4$.

If $\frac{125}{729}$ in exponential form is ${\left(\frac{5}{9}\right)}^k$, then find the value of $k$.

Write the following in usual form.
$8.08\times {10}^3$

If the number $\mathrm{6,75},\mathrm{43,000}$ can be written in standard form as $m\times {10}^7$, then find the value of $m$. (correct up to $4$ decimal places )

If the value of the following expressions is $\frac{1}{k}$, find the value of $k$.
${\left(\frac{4}{3}\right)}^2\times {\left(\frac{1}{2}\right)}^4$

If the value of the expression ${\left(\frac{6}{9}\right)}^2$ is of the form $\frac{4}{k}$, then find the value of $k$.

One hectare is equal to $\mathrm{10,000} \text{sq. m}$. If this is expressed in $\mathrm{sq}. \mathrm{cm}$ and written in scientific notations, then it will be $1\times {10}^a \mathrm{sq}. \mathrm{cm}$, then find the value of $a$.

Express the following in usual form.
$3.45\times {10}^8$

Express the following in usual form.

$5.23\times {10}^4$

If the standard form $100$ is $a\times {10}^b$, find $a+b$.

If $345$ can be expressed in standard form as $3.45\times {10}^a$, then find the value of $a$.

If $\mathrm{12,54,36,000}$ can be represented in standard form as $a\times {10}^b$, then find the value of $b$.

$27\left[{\left(2^{-1}\times 3^{-1}\right)}^2\times {\left(\frac{-3}{8}\right)}^{-1}\right]=$_____.

If $\frac{x^2}{y^4}$ can be expressed as power of rational number in the form ${\left(\frac{x^m}{y^n}\right)}^k$, then find the value of $k+m+n$.

$\frac{a^4}{b^4}=(\frac{a}{b}{)}^k$, then find the value of $k$.

If $\frac{-27}{125}$ can be expressed as power of rational number in the form ${\left(\frac{k}{5}\right)}^m$, then find the value of $k+m$.