Exponents Calculator
How to use the ‘Exponents Calculator’?
Follow the steps mentioned to use the exponents calculator:
Step 1: Choose ‘Finding Value’ or ‘Evaluating Expression’ with the given button between them.
Step 1: Enter either the product or exponent into the respective input box (if ‘Finding Value’ is selected).
Or
Enter the expression into the input box (if ‘Evaluating Expression’ is selected)
Step 4: Click on the ‘Solve’ button to obtain the value.
Step 5: Click on the ‘Show Steps’ button to know the stepwise solution to find the final value.
Step 6: Click on the refresh button to enter new inputs and start again.
Step 7: Click on the ‘Example’ button to play with different or random input values.
Step 8: Click on the ‘Explore’ button to understand how the exponential expansion of a value is visually displayed.
Step 9: When on the ‘Explore’ page, click on the ‘Calculate’ button if you want to go back to the calculator.
What is an Exponent?
The exponent of a power indicates the number of times the base is used as a factor. A power is a product of repeated factors. The base of a power is the common factor.
For example: \(x^{5}\)
So, \(x^{5}\)
is called power.
x is called base.
And 5 is called exponent.
Solved Examples:
Example 1: Find the value of the product 4 × 4 × 4 × 4.
Solution:
4 is used as a factor 4 times, its exponent is 4.
4 × 4 × 4 × 4
\(\Rightarrow 4^{4}\)
\(\Rightarrow 256\)
Example 2: Find the value of the product (-5)(-5)(-5).
Solution:
(-5) is used as a factor 3 times, its exponent is 3.
(-5)(-5)(-5)
\(\Rightarrow \left ( -5 \right )^{3}\)
\(\Rightarrow -125\)
Example 3: Find the value of the power \(6^{5}\)
Solution:
6 has an exponent as 5.
So, 6 will be used as a factor 5 times.
\(6^{5}= 6 \times 6 \times 6 \times 6 \times 6\)
= 7776
Example 4: Find the value of the power \(\left ( -10 \right )^{6}\)
Solution:
(-10) has an exponent as 6.
So, (-10) will be used as a factor 6 times.
\(\left ( -10 \right )^{6} = \left ( -10 \right )\times \left ( -10 \right )\times \left ( -10 \right )\times \left ( -10 \right )\times \left ( -10 \right )\)
= 1000000
Example 5: Evaluate the expression \(2 \times 2 \times 2 \times 2 \times 3 \times 3 \times x \times y \times y\)
Solution:
\(2 \times 2 \times 2 \times 2 \times 3 \times 3 \times x \times y \times y\)
\(= 8 \times 9 \times x \times y \times y \)
\(= 72xy^{2}\)
Example 6: Evaluate the expression \(p \times p \times p \times q \times q\times r \times r \times r\).
Solution:
\(p \times p \times p \times q \times q\times r \times r \times r\)
\(= p^{3} q^{2} r^{3}\)
To express the repeated multiplication of a number in a precise form and in a simpler manner, we use exponents. Also, exponents are used to express larger quantities, such as to represent the quantity of RBCs and WBCs in our blood, the distance of planets from the sun, the number of microbes in a given quantity of lake water and so on.
The value of the power with exponent 0 is always equal to 1.
To represent a very small quantity, we use negative exponents. For example, the diameter of an atom in meters.
In mathematics, we come across situations where two or more powers are multiplied or divided. To simplify these powers we apply the laws of exponents.