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3 years ago

2O POINTS, PLEASE HELP!! Complete the equation. (4x)^-2 (4x)^3 (4x)^9 = 4x [ ]a0

Mathematics

1 answer:

Vladimir79 [104]3 years ago

5 0

Answer:

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Step-by-step explanation:

(4x)¯² (4x)³ (4x)⁹

The above expression can be simplified as follow:

Recall:

When we have two or more index number with same base and a multiplication sign in between them, we easily simply by adding the index number together while keeping the base constant. This is illustrated below:

a^m x a^n = a^(m + n)

Therefore,

(4x)¯² (4x)³ (4x)⁹ = (4x)^(-2 + 3 +9)

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

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Find the greatest common divisor of 100 and 254, using • prime factorization- • euclidean algorithm-

larisa [96]

Via prime factorization:

$100=10^2=2^2\cdot5^2$
$254=2\cdot127$

of which the only common factor is a single power of 2, so $\mathrm{gcd}(100,254)=2$ .

Via the Euclidean algorithm:

$254=2\cdot100+54$
$100=1\cdot54+46$
$54=1\cdot46+8$
$46=5\cdot8+6$
$8=1\cdot6+2$
$6=3\cdot2+0$

which means $\mathrm{gcd}(100,254)=2$ , as expected.

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Rina8888 [55]

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Read 2 more answers

Find the solution for this system of equations.<br> 2x + 4y = 8<br> x = 3y - 6

Sergio039 [100]

Answer:

x = 0 , y = 2

Step-by-step explanation:

Solve the following system:

{2 x + 4 y = 8 | (equation 1)

x = 3 y - 6 | (equation 2)

Express the system in standard form:

{2 x + 4 y = 8 | (equation 1)

x - 3 y = -6 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + 4 y = 8 | (equation 1)

0 x - 5 y = -10 | (equation 2)

Divide equation 1 by 2:

{x + 2 y = 4 | (equation 1)

0 x - 5 y = -10 | (equation 2)

Divide equation 2 by -5:

{x + 2 y = 4 | (equation 1)

0 x+y = 2 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{x+0 y = 0 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 0 , y = 2

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