Question

Express the number $4 \times 4 \times 4 \times 4 \times 4 \times 4 \times a \times a \times a \times a$ in the exponential form?

Answer 1

Hint: We will first understand the definition and form of exponential. We will count the number of occurrences of each term and put this number of occurrences as power and the number will become its base.

Complete step-by-step solution:
When a number or a word is multiplied by itself a number of times, the expression that expresses this repeated multiplication is referred to as a power. The repeated multiplication of 3 for two times, for example, can be written as $3 \times 3 = {3^2}$ . The number 3 is known as the base, whereas the number 2 is known as the exponent.
We have $4 \times 4 \times 4 \times 4 \times 4 \times 4 \times a \times a \times a \times a$ and we will express it in exponential form.
$ = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times a \times a \times a \times a$
We have 4 occurs 6 times and a occurs 4 times, so
${\left( 4 \right)^6} \times {\left( a \right)^4}$
Hence, the expression $4 \times 4 \times 4 \times 4 \times 4 \times 4 \times a \times a \times a \times a$ in exponential form is ${\left( 4 \right)^6} \times {\left( a \right)^4}$.

Note: We have power and base in exponential form. The number written in superscript is called power, while the number written down to power is called base. The base is multiplied by p times (p=power) when an exponent is used. When the powers of two exponents with the same base are multiplied and divided, the powers are added and subtracted respectively.