Zero negative exponents
Introduction:
Exponents in math are a proficient technique to convey repeated multiplication of the similar number. Particularly powers of 10 used to convey very large and very small numbers in a technical manner. Exponential information is much more proficient for conveying numeric or quantitative information. Now let us notice about the zero and negative exponents.
Rules for Exponents:
The following rules involved in exponents,
• A whole number exponent is the shorthand for recurring multiplication of a number times itself; for example, 54 = 5 x 5 × 5 × 5
• An exponent concerns to its instant base. For example, in the expression 5 + 24, the exponent 4 concerns only to the 2, so the expression is equivalent to 5 + (2 x 2 x 2 x 2). However, in the expression (5 + 2)4, the 4 is an exponent of the quantity 5 +2 and it is evaluated as (5 + 2) x (5 + 2) x (5 + 2) x (5 + 2), or 7 x 7 x 7 x 7.
• The exponentiation is recurring multiplication; it also is completed before addition and subtraction.
Example problems for zero negative exponents:
Example in zero exponents 1:
The Zero Exponents
x0 = 1
70 = 1
The any power of zero is always equal to 1
Example in zero exponents 2:
Zero exponents using the quotient rule:
`5^4/5^4` = 54×5-4 = 50 = 1
Example in negative exponents:
3) Simplifying the equation: a-4
Solution:
a-4 = `a^-4/1`
= `1/a^4`
`1/a^-3` = `1/(1*a^-3)`
= `a^3/1`
= a3
Negative exponents produce extra steps in the simplification process.
4) Simplify the following: `x^-4/x^-9`
Solution:
The negative exponents tell to move the bases, so: `x^-4/x^-9` = `x^9/x^4`
Simplifying the equation
`x^9/x^4` = x5
5) Express the number 6-1
Solution:
Step 1: We can’t modify the base. When we shift the negative exponent in to the denominator it becomes positive.
Step 2: 6-1 = so it can be written as `1/6` .
6) Express the number `4^-2/4^-4` .
Solution:
Step 1: We can’t modify the base .When we shift the negative exponent in to the denominator it becomes positive.
Step 2: So we get `4^4/4^2` .
Step 3: When we shorten we obtain 42 = 16
7) Solve: 6-3
Solution:
6-3 = `1/6^3`
= `1/(6*6*6)`
= `1/216`
= 0.004629.
I like to share this Negative Exponents Rules with you all through my blog.
Exponents in math are a proficient technique to convey repeated multiplication of the similar number. Particularly powers of 10 used to convey very large and very small numbers in a technical manner. Exponential information is much more proficient for conveying numeric or quantitative information. Now let us notice about the zero and negative exponents.
Rules for Exponents:
The following rules involved in exponents,
• A whole number exponent is the shorthand for recurring multiplication of a number times itself; for example, 54 = 5 x 5 × 5 × 5
• An exponent concerns to its instant base. For example, in the expression 5 + 24, the exponent 4 concerns only to the 2, so the expression is equivalent to 5 + (2 x 2 x 2 x 2). However, in the expression (5 + 2)4, the 4 is an exponent of the quantity 5 +2 and it is evaluated as (5 + 2) x (5 + 2) x (5 + 2) x (5 + 2), or 7 x 7 x 7 x 7.
• The exponentiation is recurring multiplication; it also is completed before addition and subtraction.
Example problems for zero negative exponents:
Example in zero exponents 1:
The Zero Exponents
x0 = 1
70 = 1
The any power of zero is always equal to 1
Example in zero exponents 2:
Zero exponents using the quotient rule:
`5^4/5^4` = 54×5-4 = 50 = 1
Example in negative exponents:
3) Simplifying the equation: a-4
Solution:
a-4 = `a^-4/1`
= `1/a^4`
`1/a^-3` = `1/(1*a^-3)`
= `a^3/1`
= a3
Negative exponents produce extra steps in the simplification process.
4) Simplify the following: `x^-4/x^-9`
Solution:
The negative exponents tell to move the bases, so: `x^-4/x^-9` = `x^9/x^4`
Simplifying the equation
`x^9/x^4` = x5
5) Express the number 6-1
Solution:
Step 1: We can’t modify the base. When we shift the negative exponent in to the denominator it becomes positive.
Step 2: 6-1 = so it can be written as `1/6` .
6) Express the number `4^-2/4^-4` .
Solution:
Step 1: We can’t modify the base .When we shift the negative exponent in to the denominator it becomes positive.
Step 2: So we get `4^4/4^2` .
Step 3: When we shorten we obtain 42 = 16
7) Solve: 6-3
Solution:
6-3 = `1/6^3`
= `1/(6*6*6)`
= `1/216`
= 0.004629.
I like to share this Negative Exponents Rules with you all through my blog.