Simplify 12 to the 16th power over 12 to the 4th power. 1212 124 112 14

Mathematics

2 answers:

EastWind [94]3 years ago

6 0

Answer:

$12^{12}$

Step-by-step explanation:

Law Incorporation [45]3 years ago

4 0

Greetings from Brasil...

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Here's our problem:

$\large{\frac{12^{16}}{12^{4}}}$

From potentiation properties:

Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ

<em>division of power of the same base: I repeat the base and subtract the exponents</em>

<em />

Bringing to our problem

12¹⁶ ÷ 12⁴

12¹⁶⁻⁴

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Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED

marin [14]

m x H = $\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]$

Step-by-step explanation:

Step 1; Multiply 5 with this matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get a matrix $\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]$

Multiply the fraction $\frac{2}{5}$ with the matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get $\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]$

Step2; Now equate corresponding values of the matrices with each other.

-5 = $\frac{-2m}{5}$ and so on. By equating we get the value of m as $\frac{25}{2}$

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get $\left[\begin{array}{ccc}2&9&-9\\\end{array}\right]$ .

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

$\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]$ . Equating the matrices from step 3 and 4 we get the value of H as $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 5; Now to find the value of m x H we need to multiply the value of $\frac{25}{2}$ with the matrix $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 6; Multiplying we get the matrix m x H = [ -25 $\frac{75}{2}$ $\frac{-25}{2}$ ]