state four laws of exponents
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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
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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1 multiply to powers
2 when we divide powers of same base this means we have to subtract the exponents
3
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