I need help please products of powers

Mathematics

2 answers:

nignag [31]3 years ago

6 0

A number raised to an exponent is called a power. Power sometimes is used to refer to the exponent alone.

(8^2)^3 is not an example of product of powers. It is the power of a power, which is a power raised to an exponent.

The powers being multiplied in (2^4)(5^4) are 2^4 and 2^5. The rule of product of powers cannot be applied here because the bases are different. Here you can apply the rule of power of a product.

Alex777 [14]3 years ago

3 0

The first one is 32,768
The second one is 10,000

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Use Gauss-Jordan elimination to solve the following linear system.

marysya [2.9K]

Just put the coefients in to a matrix

1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14

$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\-2&2&-3|-14\end{array}\right]$
mulstiply 2nd row by -1 and add to 3rd
$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&2&0|-6\end{array}\right]$
divde last row by 2
$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]$
multiply 2rd row by 6 and add to top one
$\left[\begin{array}{ccc}1&0&-3|-14\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]$
multiply 1st row by -1 and add to 2nd
$\left[\begin{array}{ccc}1&0&-3|-14\\-3&0&0|6\\0&1&0|-3\end{array}\right]$
divide 2nd row by -3
$\left[\begin{array}{ccc}1&0&-3|-14\\1&0&0|-2\\0&1&0|-3\end{array}\right]$
mulstiply 2nd row by -1 and add to 1st row
$\left[\begin{array}{ccc}0&0&-3|-12\\1&0&0|-2\\0&1&0|-3\end{array}\right]$
divide 1st row by -3
$\left[\begin{array}{ccc}0&0&1|4\\1&0&0|-2\\0&1&0|-3\end{array}\right]$

rerange
$\left[\begin{array}{ccc}1&0&0|-2\\0&1&0|-3\\0&0&1| 4\end{array}\right]$

x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)

B is answer

7 0

3 years ago

Solve 2(b − 3) ≥ 3(3 − b) and describe the graph of the solution. Show all your work.

solong [7]

Answer:

$\large\boxed{b\geq3\to b\in[3,\ \infty)}$

Step-by-step explanation:

$2(b-3)\geq3(3-b)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(2)(b)+(2)(-3)\geq(3)(3)+(3)(-b)\\\\2b-6\geq9-3b\qquad\text{add 6 to both sides}\\\\2b-6+6\geq9+6-3b\\\\2b\geq15-3b\qquad\text{add}\ 3b\ \text{to both sides}\\\\2b+3b\geq15-3b+3b\\\\5b\geq15\qquad\text{divide both sides by 5}\\\\\dfrac{5b}{5}\geq\dfrac{15}{5}\\\\b\geq3$