Basics of Exponents

How many zeros are there in ${100}^{11}$?

If $a=2$ and $b=3$, then find the value of the ${\left(ab\right)}^b$.

Simplify ${\left(\frac{5}{9}\right)}^2\times {\left(\frac{3}{5}\right)}^3\times {\left(\frac{3}{5}\right)}^0$.

What is the value of $ m$ in the equation $ {4}^{\text{m}-1}\times {5}^{\text{m}-2}=80$?

Which of these is the value of $ \text{x}$ in the equation $ {x}^{2}\times {x}^{3/2}={2}^{7}$?

What is the value of $ y$ in the equation $ {\left(\frac{1}{3}\right)}^{\text{y}}\times {\left(\frac{1}{3}\right)}^{2\text{y}}={\left(\frac{1}{3}\right)}^{4-\text{y}}$?

Solve for $ x:$

$ 45\times 25\times 3={15}^{\text{x}}$

Given, $ {3}^{\text{n}}\times {4}^{2\text{n}+1}=\frac{1}{12}$

What is the value of $ \text{n}$?

What is the value of $ t$ if $ {\left(5t\right)}^{3}=1000$?

If $ {3}^{3+\text{n}}=27$, what is the value of $ {3}^{\text{n}}$?

$ m$ is a number such that $ {7}^{\text{m}+3}=49$

Which of these equations is true?

If $ {\left({5}^{2}\right)}^{4}={5}^{\text{m}}$, What is the value of $ m$ ?

If $ {{(2}^{3})}^{\text{x}}={y}^{\text{x}}$, what is the value of $ y$ ?

By what number should $ \frac{1}{2}$ be DIVIDED to get $ {2}^{-3}$?

By which of these numbers, must $ {\left(-4\right)}^{-1}$ be multiplied to get $ \frac{1}{12}$?

Which of these is the simplified form of $ \frac{{\left(3a\right)}^{2}}{9a}$ ?

Evaluate:

$ \frac{{a}^{x}}{{a}^{y+z}}\times \frac{{a}^{y}}{{a}^{x+z}}\times \frac{{a}^{z}}{{a}^{x+y}}$