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How to express a number as a power of 2?

  • Last Updated : 22 Sep, 2021

Mathematics is not only about numbers but it is about dealing with different calculations involving numbers and variables. This is what basically is known as Algebra. Algebra is defined as the representation of calculations involving mathematical expressions that consist of numbers, operators, and variables. Numbers can be from 0 to 9, operators are the mathematical operators like +, -, ×, ÷, exponents, etc, variables like x, y, z, etc.

Exponents and Powers

Exponents and powers are the basic operators used in mathematical calculations, exponents are used to simplifying the complex calculations involving multiple self multiplications, self multiplications are basically numbers multiplied by themselves. For example, 7 × 7 × 7 × 7 × 7, can be simply written as 75. Here, 7 is the base value and 5 is the exponent and the value is 16807. 11 × 11 × 11, can be written as 113, here, 11 is the base value and 3 is the exponent or power of 11. The value of 113 is 1331.

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Exponent is defined as the power given to a number, the number of times it is multiplied by itself. If an expression is written as cxy where c is a constant, c will be the coefficient, x is the base and y is the exponent. If a number say p, is multiplied n times, n will be the exponent of p. It will be written as



p × p × p × p … n times = pn

Basic rules of Exponents

There are certain basic rules defined for exponents in order to solve the exponential expressions along with the other mathematical operations, for example, if there are the product of two exponents, it can be simplified to make the calculation easier and is known as product rule, let’s look at some of the basic rules of exponents,

  • Product Rule ⇢ an + am = an + m
  • Quotient Rule ⇢ an / am = an – m
  • Power Rule ⇢ (an)m = an × m or m√an = an/m
  • Negative Exponent Rule ⇢ a-m = 1/am
  • Zero Rule ⇢ a0 = 1
  • One Rule ⇢ a1 = a

How do you express a number as a power of 2?

Solution:

Any number having a power of 2 can be written as the square of that number. The square of a number of a number is the number multiplied by itself, square of the number is represented as the exponent 2 on that number. If square of x has to be written, it will be x2. For instance, the square of 3 is represented as 52 and is equal to 5 × 5 = 25. Another example can be the square of 12, represented as 122, is equal to 12 × 12 = 144. Lets take the number 3, now 3 as the power of 2 will be represented as,

32 = 3 × 3

= 9

Therefore, 9 is the 2nd power of 3.



Hence, it can be concluded that any number as a power of 2 can be represented as the square of that number. 

Sample Question

Question 1: Solve the expression, 52 – 32.

Solution:

To solve the expression, first solve the 2nd powers on the numbers and then subtract the second term by the first term. However, the same problem can be solved in an easier way by simply applying a formula, the formula is,

x2 – y2 = (x + y)(x – y)

52 – 32 = (5 + 3)(5 – 3)

= 8 × 2

= 16

Question 2: Solve the expression, 102 – 62.

Solution:



To solve the expression, first solve the 2nd powers on the numbers and then subtract the second term by the first term. However, the same problem can be solved in an easier way by simply applying a formula, the formula is,

x2 – y2 = (x + y)(x – y)

102 – 62 = (10 + 6)(10 – 6)

= 16 × 4

= 64

Question 3: Solve the expression, 82 + 22.

Solution:

To solve the expression, first solve the 2nd powers on the numbers and then add the second term by the first term.

82 + 22 = (8 × 8) + (2 × 2)

= 64 + 4

= 68

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