Today, you'll know how the concept in solving indices math, we number is said to in index form( singular ), when such number or letter multiplies its self lots of time.
This means, any number raised to power of any kind must be multiplied, lots times.Something like these:
y² = y x y
t³ = t x t x t
Not , y + y nor t + t + t
This means, y is raised to the power of 2, we multiplied it with the same number raised, the same thing with t.
In mathematics, Index is the same as exponent or power. To simplify, we say indices is the plural of index.
Laws of Indices
The following are some typical examples of some laws of indices
1. k² x k² = k²⁺² ( addition laws)
2. tˣ ÷ tˠ = .tˣ⁻ˠ = ( subtraction laws)
3. (pᵸ)ⁿ = pᵸⁿ ( multiplication laws)
4. bº = 1
When ever you're asked to solve any mathematics on indices use the laws formation, applied the rules / instructions they will all work out.
Simplify the following
a. k² x k²
b. 2d² x 3d³
c. 20y² ÷ 10y³
d. 𝑥⁻³ x 𝑥⁵
e. m⁵ ÷ m²
Solution
a. k² x k²
= k²⁺²
= k⁴ ------ addition rules
b. 2d² x 3d³
= ( 2 x 3 )x d² x d³
= 6 x d²⁺³
= 6d⁵ ------- multiplication and addition laws
c. 20y² ÷ 10y³
20
= ----------- x y³⁻²
10
= 2 x y
= 2y ------------- Division and subtraction
Can you see how i applied all the rules given in each question, do the same. Some others examples are as follow:
a. 4 x a ⁻¹/²
4
-------
✓a
b. 5х⁻²
workings
5х⁻²
5 1 5 x 1
-------- x ----- = -----------
1 х² 1 x х²
5
= ---------
х²
Note
m⁻²
1
-------- also ,
m²
m⁻1 is
1
--------
m
Now solve these
a. (5p)⁻²
b. 36y³
-----------
2y⁻⁹
c. 5uv x 7w²
d. xy⁻²
If have you questions, please put them in the comment box.
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