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b can be equal to 3 or 4:
25*3*3 - 3*3*3*3 = 225 - 81 = 144.
25*4*4 - 4*4*4*4 = 400 - 256 = 144.
That is correct. I knew it was 3 and 4.
But I need the method by which one can calculate the answer.
Thank you.
You can rearrange the terms set this up as a quadratic equation and solve for b2
Let x = b2, then
25b2 - b4 = 144 can be rewritten as
-x2 + 25x -144 = 0, and a = -1, b = 25, and c = -144
Plugging into the quadratic equation, we get:
x = (-25 +/- sqrt(25^2 - 4*-1*-144)) / 2*-1
x = (-25 +/- sqrt(625 - 576) ) / -2
x = (-25 +/- 7) / -2
x = -18/-2 = 9, or
x = -32/-2 = 16
and since x = b2, then b = 3 or 4
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What does B to the 4Th power equal?
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How do you calculate integers to the power of -8.2 or other minus decimal places?
Example: Let's say b-8.2, where b is an integer. First step, turn the negative exponent to a positive one, and then use the laws of exponents. b-8.2 = 1/b8.2 = 1/b8+1/5 = 1/[b8b1/5] = 1/b8 * 1/b1/5 = 1/b8 * {1(b4/5)/[(b1/5)(b4/5)]} = 1/b8 * b4/5/b(1/5)+(4/5) = 1/b8 * b4/5/b5/5 = 1/b8 * b4/5/b = b4/5/b8+1 = b4/5/b9
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Because of the way this is written, there are two possibilities in simplifying. Choose the one that applies:a4 - ab4 = a(a3 - b4); here, only the 'b' term is raised in the second term, so a1 is the only thing we can take out.a4 - (ab)4 - a4(1 - b4). Because a4 is a part of both terms, it can be removed from both as well.
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What does B to the 4Th power equal?
B4 or B*B*B*B
What letter and number mean 'ahead of' or 'in front of'?
b4
How do you calculate integers to the power of -8.2 or other minus decimal places?
Example: Let's say b-8.2, where b is an integer. First step, turn the negative exponent to a positive one, and then use the laws of exponents. b-8.2 = 1/b8.2 = 1/b8+1/5 = 1/[b8b1/5] = 1/b8 * 1/b1/5 = 1/b8 * {1(b4/5)/[(b1/5)(b4/5)]} = 1/b8 * b4/5/b(1/5)+(4/5) = 1/b8 * b4/5/b5/5 = 1/b8 * b4/5/b = b4/5/b8+1 = b4/5/b9
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