Q57. - Algebra 1

Question

 Evaluate the expression ${\left(2.5\right)}^{\mathbf{2}}$.

Step-by-Step Solution

Answer

The value of expression is 6.25.

Step 1. Concept of exponent and base.

In the expression $a^x$, a is the base and x is exponent.

The power is the result of repeated multiplication of the same factor. 

The expressions a^x this means that a has been used as a factor x times.

Step 2. Example of exponent.

Example: Write the product $5\cdot 5\cdot 5\cdot 5$ in exponent.

For: $5\cdot 5\cdot 5\cdot 5$: the base a = 5 and multiplied by 4 times. 

In repeated multiplication: $5\cdot 5\cdot 5\cdot 5$ in exponent form 

Step 3. Calculation.

First multiply the numbers normally as whole numbers then count the total number of digits after the decimal in each number and place the decimal point before the same number of digits from right to left in the resultant product.

So, we have

$\begin{array}{l}{\left(25\right)}^2=25\times 25\\ {\left(25\right)}^2=625\\ \text{Thus}\\ {\left(2.5\right)}^2=\left(2.5\right)\times \left(2.5\right)\\ {\left(2.5\right)}^2=6.25\end{array}$

Therefore, the solution of the expression ${\left(2.5\right)}^2$ is 6.25.