Question

Evaluate the expression

${\mathbf{3}}^8\mathbf{\times }{\mathbf{3}}^5$

$\frac{{\mathbf{10}}^7}{{\mathbf{10}}^4}$

${\left({\mathbf{3}}^5\right)}^4$

Short answer

1. The value of expression $3^8\cdot 3^5$is $3^{13}$
2. The value of expression$\frac{{10}^7}{{10}^4}$is 1000.

3. The value of expression${\left(3^5\right)}^4$is $3^{20}$.

Step-by-step solution

a. Step-1 – Simplify the given expression

On simplifying the given expression$3^8\cdot 3^5$,

$\begin{array}{c}{3}^8\cdot 3^5={\left(3\right)}^8\cdot {\left(3\right)}^5\\ ={\left(3\right)}^{8+5}\end{array}$

Step-2 – Further simplifying

$\begin{array}{c}{3}^8\cdot 3^5={\left(3\right)}^{13}\\ =3^{13}\end{array}$

Step-3 – Description of steps

The value of expression $3^8\cdot 3^5$is$3^{13}$.

Step-1 – Simplify the given expression

On simplifying the given expression$\frac{{10}^7}{{10}^4}$,

$\begin{array}{c}\frac{{10}^7}{{10}^4}={\left(10\right)}^{7-4}\\ ={\left(10\right)}^3\end{array}$

Step-2 – Further simplifying

$\begin{array}{c}\frac{{10}^7}{{10}^4}=\left(10\right)\left(10\right)\left(10\right)\\ =1000\end{array}$

Step-3 – Description of steps

The value of expression$\frac{{10}^7}{{10}^4}$ is 1000.

Step-1 – Simplify the given expression

On simplifying the given expression${\left(3^5\right)}^4$,

$\begin{array}{c}{\left(3^5\right)}^4={\left(3\right)}^{\left(5\right)\left(4\right)}\\ ={\left(3\right)}^{20}\end{array}$

Step-2 – Further simplifying

${\left(3^5\right)}^4=3^{20}$

Step-3 – Description of steps

The value of expression${\left(3^5\right)}^4$is$3^{20}$.