Answer:
Proved (See Explanation)
Step-by-step explanation:
Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is done as follows
From laws of indices;
aᵐ⁺ⁿ = aᵐ * aⁿ.
So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.
becomes
Factorize
3ⁿ * 5
5(3ⁿ)
<em>The expression can not be further simplified.</em>
<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>
Answer:
All 3 are right triangles.
Step-by-step explanation:
In a right triangle c^2 = a^2 + b^2 where c is the longest side. ( by Pythagoras).
a) 3^2 = 9, 6^2 = 36 and √27 ^ 2 = 27
36 = 9 + 27
So this is a right triangle.
b)
17^2 = 289, 15^2 = 225 and 8^2 = 64
289 = 225 + 64
Also right triangle.
c) √50 ^ 2 = 50, 5^2 = 25 and 5^2 = 25
So also right triangle.
Step-by-step explanation:
This isn't. a true identity.
The value of the expression given as [3² * 3⁻⁵]/[5⁻²] is 25/27
<h3>How to evaluate the expression?</h3>
The expression is given as:
3 squared times 3 to the power of negative 5 end quantity over 5 to the power of negative two
Rewrite properly as:
[3² * 3⁻⁵]/[5⁻²]
Apply the negative exponent law of indices
So, we have
[3² * 3⁻⁵]/[5⁻²] = [5²]/[3⁻² * 3⁵]
Apply the exponent law of indices
[3² * 3⁻⁵]/[5⁻²] = [5²]/[3³]
This gives
[3² * 3⁻⁵]/[5⁻²] = 25/27
Hence, the value of the expression given as [3² * 3⁻⁵]/[5⁻²] is 25/27
Read more about expressions at:
brainly.com/question/723406
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