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4k^2(4^-1+4k^-2)
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Answer:
K2+16 Make me Brainlist answer please
Step-by-step explanation:
1): "^-2" was replaced by "^(-2)". 1 more similar replacement(s)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(4 • (k2)) • ((4-1) + 22k(-2))
Step 2 :
2.1 4 = 22
(4)-1 = (22)(-1) = (2)(-2)
Equation at the end of step 2 :
(4 • (k2)) • ((2)(-2) + 22k(-2))
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 22 as the denominator :
22k(-2) 22k(-2) • 22
22k(-2) = ——————— = ————————————
1 22
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 + 22k(-2) • 4 1 + 16k(-2)
——————————————— = ———————————
4 4
Equation at the end of step 3 :
(1 + 16k(-2))
(4 • (k2)) • —————————————
4
Step 4 :
Equation at the end of step 4 :
(1 + 16k(-2))
22k2 • —————————————
4
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
1 + 16k(-2) = k(-2) • (k2 + 16)
Polynomial Roots Calculator :
6.2 Find roots (zeroes) of : F(k) = k2 + 16
Polynomial Roots Calculator is a set of methods aimed at finding values of k for which F(k)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers k which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 16.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8 ,16
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 17.00
-2 1 -2.00 20.00
-4 1 -4.00 32.00
-8 1 -8.00 80.00
-16 1 -16.00 272.00
1 1 1.00 17.00
2 1 2.00 20.00
4 1 4.00 32.00
8 1 8.00 80.00
16 1 16.00 272.00
Polynomial Roots Calculator found no rational roots
Multiplying exponential expressions :
6.3 k2 multiplied by k(-2) = k(2 + (-2)) = k0 = 1 Any number to the zero power is 1
Canceling Out :
6.4 Canceling out 22 as it appears on both sides of the fraction line
Final result :
k2 + 16
Answer:
1): "^-2" was replaced by "^(-2)". 1 more similar replacement(s)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(4 • (k2)) • ((4-1) + 22k(-2))
Step 2 :
2.1 4 = 22
(4)-1 = (22)(-1) = (2)(-2)
Equation at the end of step 2 :
(4 • (k2)) • ((2)(-2) + 22k(-2))
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 22 as the denominator :
22k(-2) 22k(-2) • 22
22k(-2) = ——————— = ————————————
1 22
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 + 22k(-2) • 4 1 + 16k(-2)
——————————————— = ———————————
4 4
Equation at the end of step 3 :
(1 + 16k(-2))
(4 • (k2)) • —————————————
4
Step 4 :
Equation at the end of step 4 :
(1 + 16k(-2))
22k2 • —————————————
4
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
1 + 16k(-2) = k(-2) • (k2 + 16)
Polynomial Roots Calculator :
6.2 Find roots (zeroes) of : F(k) = k2 + 16
Polynomial Roots Calculator is a set of methods aimed at finding values of k for which F(k)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers k which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 16.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8 ,16
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 17.00
-2 1 -2.00 20.00
-4 1 -4.00 32.00
-8 1 -8.00 80.00
-16 1 -16.00 272.00
1 1 1.00 17.00
2 1 2.00 20.00
4 1 4.00 32.00
8 1 8.00 80.00
16 1 16.00 272.00
Polynomial Roots Calculator found no rational roots
Multiplying exponential expressions :
6.3 k2 multiplied by k(-2) = k(2 + (-2)) = k0 = 1 Any number to the zero power is 1
Canceling Out :
6.4 Canceling out 22 as it appears on both sides of the fraction line
Final result :
k2 + 16
Step-by-step explanation:
Hope this answer will help you.