Math, asked by ranasalman70510, 9 months ago

state any four laws of exponents for real number

Answers

Answered by BrainlyEmpire
6

Answer:

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Step-by-step explanation:

Laws of Exponents. When multiplying like bases, keep the base the same and add the exponents. When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent

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Answered by izmahilalkhan08
0

Answer:

1. Product law

According to the product law of exponents when multiplying two numbers that have the same base then we can add the exponents

am × an= a m+n

where a, m and n all are natural numbers. Here the base should be the same in both the quantities. For example,

2³ × 24 = 27

22/3 × 21/5 = 2 2/3 + 1/5 = 2(10+3)/15 . We get, = 212/15

(-6) 3 x (-6) 2 = (-6) 3+2 = (-6) 5

2. Quotient Law

According to the quotient law of exponents, we can divide two numbers with the same base by subtracting the exponents. In order to divide two exponents that have the same base, subtract the power in the denominator from the power in the numerator.

am ÷ an = a m-n

where a, m and n all are natural numbers. Here the base should be the same in both the quantities. For example,

25 ÷ 23 = 2²

p6 ÷ p2 = p 6 – 2 = p 4

3. Power Law

According to the power law of exponents if a number raise a power to a power, just multiply the exponents

(am)n = am×n

Here there is one base a and two powers m and n. For example, ( 53 )2 = 53×2 = 56

Important Points to Remember on Exponent Rules

1an = a-n. A non zero base raised to a negative exponent is equal to the reciprocal of the base raised to the positive exponent or 1a−n = a+n

a0 = 1. This says that anything raised to the zero power is 1. For example, 50= 1, (1000) 0 = 1

a1 = a

Power of Product

The power of product rule states that: (ab)m = am × bm, a and b are positive real numbers and m is the rational number. For example, ( 2 × 5)10 = 210 × 510

Power of Quotient

The power of product rule states that:

ab^n = anbn

Or, 25^12 = 212512

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