Question

Evaluate the expression

1. ${\mathbf{5}}^3\mathbf{\times }\mathbf{5}$
2. ${\mathbf{5}}^4\mathbf{\times }{\mathbf{5}}^{-2}$
   C.${\left({\mathbf{2}}^2\right)}^3$
   

Short answer

1. The value of expression $5^3\cdot 5$is 625.
2. The value of expression ${\left(5\right)}^4\cdot {\left(5\right)}^{-2}$is 25.
3. The value of expression ${\left(2^2\right)}^3$is 64.

Step-by-step solution

Step-1 – Simplify the given expression

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

$\begin{array}{c}{5}^3\cdot 5={\left(5\right)}^3\cdot {\left(5\right)}^1\\ ={\left(5\right)}^{3+1}\end{array}$

Step-2 – Further simplifying

$\begin{array}{c}{5}^3\cdot 5={\left(5\right)}^4\\ =625\end{array}$

Step-3 – Description of steps

The value of expression$5^3\cdot 5$is 625.

Step-1 – Simplify the given expression

On simplifying the given expression${\left(5\right)}^4\cdot {\left(5\right)}^{-2}$,

$\begin{array}{c}{\left(5\right)}^4\cdot {\left(5\right)}^{-2}=\frac{{\left(5\right)}^4}{{\left(5\right)}^2}\\ ={\left(5\right)}^{4-2}\end{array}$

Step-2 – Further simplifying

$\begin{array}{c}{\left(5\right)}^4\cdot {\left(5\right)}^{-2}={\left(5\right)}^2\\ =25\end{array}$

Step-3 – Description of steps

The value of expression${\left(5\right)}^4\cdot {\left(5\right)}^{-2}$is 25.

C.Step-1 – Simplify the given expression

On simplifying the given expression${\left(2^2\right)}^3$,

$\begin{array}{c}{\left(2^2\right)}^3={\left(2\right)}^{\left(2\right)\left(3\right)}\\ ={\left(2\right)}^6\end{array}$

Step-2 – Further simplifying

$\begin{array}{c}{\left(2^2\right)}^3=\left(2\right)\left(2\right)\left(2\right)\left(2\right)\left(2\right)\left(2\right)\\ =64\end{array}$

Step-3 – Description of steps

The value of expression${\left(2^2\right)}^3$is 64.