Math, asked by kunal24bharti, 1 month ago

Write LAWS OF EXPONENTS and write one example for each law.​

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Answered by veeksha74
0

Answer:

Step-by-step explanation:

Rules of Exponents With Examples

Exponents follow certain rules that help in simplifying expressions which are also called its laws. Let us discuss the laws of exponents in detail.

Product With the Same Bases

As per this law, for any non-zero term a,

am×an = am+an

where m and n are real numbers.

Example 1: What is the simplification of 55 × 51 ?

Solution: 55 × 51 = 55+1 = 56

Note: We can state that the law is applicable for negative terms also. Therefore the term m and n can be any integer.

Quotient with Same Bases

As per this rule,

am/an = am-n

where a is a non-zero term and m and n are integers.

Example 3: Find the value when 10-5 is divided by 10-3.

Solution: As per the question;

10-5/10-3

= 10-5-(-)3

= 10-5+3

= 10-2

= 1/100

Power Raised to a Power

According to this law, if ‘a’ is the base, then the power raised to the power of base ‘a’ gives the product of the powers raised to the base ‘a’, such as;

(am)n = amn

where a is a non-zero term and m and n are integers.

Example 4: Express 83 as a power with base 2.

Solution: We have, 2×2×2 = 8 = 23

Therefore, 83= (23)3 = 29

Product to a Power

As per this rule, for two or more different bases, if the power is same, then;

an bn = (ab)n

where a is a non-zero term and n is the integer.

Example 5: Simplify and write the exponential form of: 1/8 x 5-3

Solution: We can write, 1/8 = 2-3

Therefore, 2-3 x 5-3 = (2 × 5)-3 = 10-3

Quotient to a Power

As per this law, the fraction of two different bases with the same power is represented as;

an/bn = (a/b)n

where a and b are non-zero terms and n is an integer.

Example 6: Simplify the expression and find the value:153/53

Solution: We can write the given expression as;

(15/5)3= 33 = 27

Zero Power

According to this rule, when the power of any integer is zero, then its value is equal to 1, such as;

a0 = 1

where ‘a’ is any non-zero term.

Example 7: What is the value of 50 + 22 + 40 + 71 – 31 ?

Solution: 50 + 22 + 40 + 71 – 31 = 1+4+1+7-3= 10

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Answered by oeiseghosh
2

Step-by-step explanation:

these are the laws I hope it helps

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