Exponents and Powers Class 7 Maths Formulas

The List of Important Formulas for Class 7 Exponents and Powers is provided on this page. We have everything covered right from basic to advanced concepts in Exponents and Powers. Make the most out of the Maths Formulas for Class 7 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Exponents and Powers Class 7 covering numerous concepts and use them to solve your Problems effortlessly.

Exponents
We can write large numbers in a short form using exponents.
For example: 10,000 = 10 × 10 × 10 × 10 = 10⁴
Here, ‘10’ is called the base and ‘4’ the exponent. The number 10⁴ is read as 10 raised to the power of 4 or simply as the fourth power of 10.
10⁴ is called the exponential form of 10,000.

(1)^{any natural number} = 1

(-1)^{an odd natural number} = -1

(-1)^{an even natural number} = +1

a^m × aⁿ = a^m+n, where m and n are whole numbers and a (≠ 0) is an integer.
This formula can be used to write answers to above questions.

For any non-zero integer a,
a^m ÷ aⁿ = a^m-n where m and n are whole numbers and m > n.

For any non-zero integer a,
(a^m)ⁿ = a^mn (where m and n are whole numbers)

For any non-zero integer a
a^m × b^m = (ab)^m (where m is any whole number)

(where m is a whole number; a and b are any non-zero integers)

a⁰ = 1 (for any non-zero integer a)
Any number (except 0) raised to the power (or exponent) 0 is 1.

Decimal Number System
10,000 = 10⁴
1000 = 10³
100 = 10²
10 = 10¹
1 = 10⁰
We can write the expansion of a number using powers of 10 in the exponent form.

Expressing Large Numbers in the Standard Form
Large numbers can be expressed conveniently using exponents. Such a number is said to be in standard form if it can be expressed as k × 10^m, where 1 ≤, k < 10 and m is a natural number.

Note that, one less than the digit count (number of digits) to the left of the decimal point in a given number, is the exponent of 10 in the standard form.

For any rational number a and positive integer n, we define aⁿ as a × a × a × …… × a (n times). aⁿ is known as the nth power of a and is read as ‘a raised to the power n’. The rational a is called the base and n is called the exponent or power.
e.g. 10,000 = 10 × 10 × 10 × 10 = 10⁴.
10 is the base and 4 is the exponent.

Multiplying Powers with the Same Base: If a is any non-zero integer and whole numbers are m and n, then a^m × aⁿ = a^m+n
e.g. 2⁴ × 2²
a = 2, m = 4, n = 2
2⁴ × 2² = 2⁴⁺² = 2⁶

Dividing Powers with the Same Base: If a is any non-zero integer and m, n are the whole number, then a^m ÷ aⁿ = a^m-n
e.g. 2⁴ ÷ 2²
a = 2, m = 4, n = 2
2⁴ ÷ 2² = 2^4-2 = 2²

Taking Power of a Power: If a is any non-zero integer and m, n are whole numbers, (a^m)ⁿ = a^mn
e.g. (6²)⁴
a = 6, m = 2, n = 4
(6²)⁴ = (6)^2×4 = 6⁸.

Multiplying Powers with the Same Exponents: If a, b are two non-zero integers and m is any whole number, then
a^m × bⁿ = (a × b)^m
e.g. 2³ × 3³
a = 2, b = 3, m = 3
2³ × 3³ = (2 × 3)³ = 6³.

Dividing Powers with the Same Exponents: If a, b are two non-zero integers and m is a whole number, then

Numbers with Exponent Zero: If a be any non-zero integer, then, a⁰ = 1

Numbers with Negative Exponent: If a is any non-zero integer, then a^-1 = \(\frac { 1 }{ a }\)
e.g. 2^-5 = \(\frac { 1 }{ { 2 }^{ 5 } }\)

In decimal number system, the exponents of 10 start from a maximum value and go on decreasing from the left to right upto 0.
e.g. 45672 = 4 × 10000 + 5 × 1000 + 6 × 100 + 7 × 10 + 2 × 1
= 4 × 10⁴ + 5 × 10³ + 6 × 10² + 7 × 10¹ + 2 × 10⁰
It is called expanded form of a number.

Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a power of 10. Such a form of a number is called its standard form.
e.g. 56782 = 5.6782 × 10000 = 5.6782 × 10⁴.
It is the standard form of 56782.