Question

Expand $ 1025.63 $ using exponents.

Answer 1

Hint: The power can be used to express mathematical equations in the short form; it is an expression that denotes the repeated multiplication of the same factor. For example - $ 2 \times 2 \times 2 $ can be expressed as $ {2^3} $ . Here, the number two is so-called the base and the exponent denotes the number of times the base is used as the factor. First we will expand the given mathematical expression and then will convert them in the form of sum of exponents.

Complete step-by-step answer:
Take the given mathematical expression: $ 1025.63 $
Now expand the above expression based on the place value for all the digits.
\[1025.63 = (1 \times 1000) + (0 \times 100) + (2 \times 10) + (5 \times 1) + (6 \times \dfrac{1}{{10}}) + (3 + \dfrac{1}{{100}})\]
Now, when the same number is multiplied twice, the value can be written as square, similarly if the same number is multiplied thrice then the cube is written.
Also, the multiplicative inverse can be defined as the reciprocal. Let us assume that “x” be any number then its multiplicative inverse can be stated as $ \dfrac{1}{x}{\text{ and }}{{\text{x}}^{ - 1}} $ .
Now, \[1025.63 = (1 \times {10^3}) + (0 \times {10^2}) + (2 \times {10^1}) + (5 \times 1) + (6 \times {10^{ - 1}}) + (3 + {10^{ - 2}})\]
This is the required solution.

Note: Be good in squares, cubes, fourth, and so on for the number. Don’t be confused between reciprocal and the additive inverse.
Remember the seven basic rules of the exponent or the laws of exponents to solve these types of questions. Make sure to go through the below mentioned rules, it describes how to solve different types of exponents problems and how to add, subtract, multiply and divide the exponents.
I.Product of powers rule
II.Quotient of powers rule
III.Power of a power rule
IV.Power of a product rule
V.Power of a quotient rule
VI.Zero power rule