Brush up on your math skills with our class 7 worksheets on exponents and powers! Through these engaging activities, you'll review key concepts to understand how to use exponent notation and calculate expressions with powers.
Introduction to Exponents and Powers.
Exponents are used to denote the repeated multiplication of a number. It is a short form for writing multiplying the same number multiple times, instead of having to write out the calculations. For example, 4 x 4 x 4 can be written as 43 which is called an exponent or power.
Multiplying and Dividing Terms with Exponents.
When you are dealing with the same base, and the exponents have different values, you will need to work out the value of each term separately. For example if you are given a problem like 53 x 52 = ? To solve this, you will then need to multiply the two terms together by multiplying their exponents. In this case it would be 3x2 which is 6. Therefore the answer to the problem is 56
Rules of Exponents: Zero, Negative, Fractional, and More.
When dealing with exponents, there are certain rules that you should keep in mind. These include; Zero Exponents often equal 1, Negative Exponents flip the base number’s sign, Fractional Exponents indicate how many times to apply the root of the base number, and more. Having a better understanding of these rules will help you understand how to solve any given problem you may face with exponents and powers!
Scientific Notation and Exponents Practice Problems.
Practice solving problems with scientific notation and exponents using our Class 7 worksheets. These worksheets provide a set of realistic practice questions that require you to use the rules for exponents you have learned, allowing you to test and hone your skills to handle the various types of calculations that come up when dealing with exponents and powers.
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Laws of Exponents class 7th
Product law: When multiplying two exponential expressions with the same base, add their exponents. That is, for any non-zero real numbers a and b and any integer m, we have:
am × an = a(m+n)
Example: 23 × 24 = 2(3+4) = 27 = 128
Quotient law: When dividing two exponential expressions with the same base, subtract their exponents. That is, for any non-zero real numbers a and b and any integer m, we have:
am ÷ an = a(m-n)
Example: 56 ÷ 52 = 5(6-2) = 54 = 625
Power law: When raising an exponential expression to another exponent, multiply their exponents. That is, for any non-zero real number a and any integers m and n, we have:
(am)n = a(m×n)
Example: (32)3 = 3(2×3) = 36 = 729
Negative exponent law: A negative exponent is equivalent to the reciprocal of the expression with the corresponding positive exponent. That is, for any non-zero real number a and any positive integer n, we have:
a(-n) = 1/(an)
Example: 2(-3) = 1/(23) = 1/8
Zero exponent law: Any non-zero base raised to the zero exponent is equal to 1. That is, for any non-zero real number a, we have:
a0 = 1
Example: 40 = 1
Exponents and Powers class 7 extra Questions ( Revision)
- Simplify the following expressions using the laws of exponents:
a) 2^3 × 2^5
b) 10^4 ÷ 10^2
- Write the following numbers in scientific notation:
- Evaluate the following expressions:
a) 3^4 × 3^2
b) (5^3 × 2^2) ÷ (2^3 × 5)
c) (2^4 × 3^2) ÷ (2^2 × 3)
- Express the following numbers in standard form:
a) 4.5 × 10^6
b) 6.7 × 10^-3
c) 8.9 × 10^2
- Simplify the following expressions:
c) (3ab^2c)^3 ÷ (9a^2b^5)
Q: What is an exponent?
A: An exponent is a mathematical notation that indicates how many times a number, called the base, is multiplied by itself.
Q: What is a power?
A: A power is an expression that represents repeated multiplication of the same factor, which is the base, with a given exponent.
Q: What are the laws of exponents?
A: The laws of exponents are a set of rules that simplify the manipulation of exponential expressions. They include the product law, quotient law, power law, negative exponent law, and zero exponent law.
Q: What is scientific notation?
A: Scientific notation is a way of expressing numbers that are very large or very small. It is written in the form a × 10^n, where a is a number between 1 and 10, and n is an integer.
Q: How do you convert a number to scientific notation?
A: To convert a number to scientific notation, you move the decimal point to the left or right until there is only one non-zero digit to the left of the decimal point. The number of places you move the decimal point determines the value of the exponent.
Q: What is the meaning of a negative exponent?
A: A negative exponent means that the base is being divided by itself a certain number of times. For example, 2^-3 means 1/(2^3) or 1/8.
Q: What is the meaning of a zero exponent?
A: A zero exponent means that the base is being multiplied by itself zero times, which results in the value of 1.
Q: How do you simplify expressions with exponents?
A: To simplify expressions with exponents, you can use the laws of exponents to combine like terms, and then evaluate the expression if possible.
Q: What are some real-world applications of exponents and powers?
A: Exponents and powers are used in many scientific and engineering fields to represent quantities that vary exponentially, such as population growth, radioactive decay, and compound interest. They are also used in computer science and cryptography to represent large numbers and perform efficient computations.