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Lemur [1.5K]
3 years ago
8

I don’t understand this help please

Mathematics
1 answer:
Elodia [21]3 years ago
3 0

Answer:

  9

Step-by-step explanation:

The first simplification we can make is to replace 6^0 with 1.

The first rules of exponents we can apply are ...

  <em>(a·b)^c = a^c·b^c</em> . . . . . . similar to the distributive property

<em>   (a^b)^c = a^(b·c)</em>

This reduces your expression to ...

  (2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}

Now we can apply another two rules of exponents:

<em>   (a^b)(a^c) = a^(b+c)</em>

<em>   1/a^b = a^-b</em>

Using these, we have ...

  =2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9

The value of the expression is 9.

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C)  The solution for the given system of equations are A(0,-5) and B(-4,3)

Step-by-step explanation:

The given system of equation are : x^{2}  + y^{2}  = 25\\2x  + y  = -5

from equation 2, we get   y = -5 - 2x .

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By ALGEBRAIC IDENTITY:

(a+b)^{2}   = a^{2}  +  b^{2}  + 2ab\\ (-5-2x)^{2} = (-5)^{2}  +  (-2x)^{2}  + 2(-5)(-2x)

or, x^{2}  + (-5-2x)^{2}  = 25  \implies x^{2} + (25  +  4x^{2}  + 20x)  = 25

or, 5x^{2}  + 20x = 0  \implies x(5x + 20) = 0

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Hence, the solution for the given system of equations are A(0,-5) and B(-4,3)

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