Rules Of Exponents And Powers
2. am ÷ an = am–n (Quotient rule)
3. (am)n = am × n (Power of a power rule)
4. (ab)m = am bm (Power of a product rule)
5. (a/b)m = am/bm (Power of a quotient rule)
6. a−m = 1/am (Negative of an exponent)
7. a0 = 1 (zero exponent rule)
8. a1 = a
EXPONENTS□
×a3×5a4×a3×5a4×a3×5a4
Examples
1. calculate 8³ ÷8²
Answer
By using the quotient rule
am ÷ an = am–n
8³ ÷8² = 83-2
= 81
2. calculate c100 ÷ c90
Answer
By using the quotient rule
am ÷ an = am–n
c100 ÷ c90 = c100–90
= c10
3. calculate 911 ÷ 97
Answer
By using the quotient rule
am ÷ an = am–n
911 ÷ 97 = 911–7
= 94
3. POWER OF A POWER RULE
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 = am × n
Examples;
1. calculate (73)5
Answer
By using the power of a power rule
(am)n = am × n
(73)5 = 73 × 5
= 715
2.calculate (b2)6
Answer
By using the power of a power rule
(am)n = am × n
(b2)6 = b2 × 6
= b12
3.calculate (32)5 * (34)3
Answer
By using the power of a power rule
(am)n = am × n
(32)5 * (34)3 = 310 * 312
Now by using the product rule
am × an = am + n
310 * 312 = 310+12
= 322
4. POWER OF A PRODUCT RULE
According to this rule, for two or more different bases, if the power is same,
then;
(ab)m = am bm
Examples:
1. calculate 1/8 x 5-3
Answer
By using the power of a product rule
(ab)m = am bm
We can write, 1/8 = 2-3
2-3 x 5-3 = (2 × 5)-3 = 10-3
2.calculate 76 x 56
Answer
By using the power of a product rule
(ab)m = am bm
76 x 56 = (7 × 5)6
= 356
3. calculate b4 x c4
Answer
By using power of a product rule
(ab)m = am bm
b4 x c4 = (bc)4
5. POWER OF A QUOTIENT RULE
According to this law, the fraction of two different bases with the same
power is
153/53 = (15/5)3
= (33) = 27
2. calculate 104/1004
Answer
By using the power of a quotient rule
(a/b)m = am/bm
104/1004 = (10/100)4
= (1/10)4
3. calculate a7/b7
Answer
By using the power of a quotient rule
(a/b)m = am/bm
a7/b7 = (a/b)7
= (a/b)7
6. NEGATIVE OF AN EXPONENT
According to this rule, if the exponent is negative, we can change
the exponent into positive by writing the same value in the denominator and the
numerator holds the value 1.
a−m = 1/am
Example:
Find the value of 2-2
Answer
By using the negative of an exponent rule
a−m = 1/am
2-2 = 1/2 2
=1/4
7. ZERO EXPONENT RULE
According to this rule, when the power of any integer is zero, then its value is equal to 1,
a0 = 1
Example:
Find the value of 70
Answer
By using the zero exponent rule
a0 = 1
70 = 1
More Problems on Laws of Exponents
1. What is the value of 50 + 22 + 40 + 71 – 31 ?
Answer; 50 + 22 + 40 + 71 – 31
= 1+4+1+7-3= 10
2. Express 83 as a power with base 2.
Answer: : We know, 8= 2×2×2 = 23
Therefore, 83= (23)3 = 29
3. What is the simplification of (−6)-4 × (−6)-7?
Answer: (−6)-4 × (−6)-7
= (-6)-4-7 = (-6)-11.
5. Find the value when 10-5 is divided by 10-3.
Answer: As per the question;
10-5/10-3
= 10-5-(-)3
= 10-5+3
= 10-2
= 1/100
SUMMARY
The exponent of a number indicates the total time to use that number in a
multiplication. For example, 8 × 8 × 8 can be expressed as 83 because 8 is
multiplied by itself 3 times. Here, 3 is the ‘exponent’ or ‘power’ which tells how
many times 8 is multiplied by itself, and 8 is the ‘base’ which represents the
number being multiplied. In short, power or exponent indicates the number of times
a number needs to be multiplied by itself. Here, the base can be any integer,
fraction or decimal. The exponent can also take up any value, be it positive or
negative. Above we all ready discussed above different exponential rules.
=
0 Comments:
Post a Comment