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The solution of the exponents is shown below.
Exponents are mathematical shorthand for multiplying a number by itself a certain number
We have that;
5^n = 1
5^n = 5^0
n = 0
2) 2^-7/2^n = 2^2
2^-7 - n = 2^2
-7 - n = 2
-n = 2 + 7
n = -9
3) 6^5 * 6^n = 6^1
6^ 5 + n = 6^1
5 + n = 1
n = 1 - 5
n = -4
4) (8^n)^7 = 8^21
8^7n = 8^21
7n = 21
n = 3
5) 4^n = (1/4)
4^n = 4^-1
n = -1
In each of the cases, we have applied the laws of the exponents as we know them.
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Rewritten by : Barada
The equation of the forms are matched as;
2⁻⁷/2ⁿ = 2², n = -9
6⁵ * 6ⁿ = 6. n = -4
(8ⁿ)⁷ = 8²¹, n = 3
4ⁿ = 1/4 , n = -1
Index forms are simply described as mathematical forms that are used to represent numbers of variables that are too large or small.
To multiply index forms, you need to add the exponents of the same bases.
To divide index forms, you need to subtract the exponents of the same bases.
From the information given, we have that;
2⁻⁷/2ⁿ = 2²
cross multiply the values
2⁻⁷ = 2²⁺ⁿ
Then,
-7 = 2 + n
n = -9
6⁵ * 6ⁿ = 6
take the exponents
5 + n= 1
n =- 4
(8ⁿ)⁷ = 8²¹
We have;
7n = 21
Make 'n' the subject
n = 3
4ⁿ = 1/4
4ⁿ = 4⁻¹
n =-1
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