Question

If (3/4)⁴ X (16/9)⁵ = (4/3)ᵏ⁺²,then the value of k is.​

Answer 1

it is so easy see the solution will be

-4+7=K+2

3=K+2

1=K

this is the answer

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Answer 2

Answer:

The value of k is 4.

Step-by-step explanation:

Here given,

${ (\frac{3}{4}) }^{4} \times ( \frac{16}{9}) ^{5} = ( \frac{4}{3} )^{k + 2}$

${ (\frac{3}{4}) }^{4} \times ( \frac{ {4}^{2} }{ {3}^{2} }) ^{5} = ( \frac{4}{3} )^{k + 2} \\ { (\frac{3}{4}) }^{4} \times ( \frac{ {4}^{2 \times 5} }{ {3}^{2 \times 5} }) = ( \frac{4}{3} )^{k + 2} \\ { (\frac{3}{4}) }^{4} \times ( \frac{ {4}^{10} }{ {3}^{10} }) = ( \frac{4}{3} )^{k + 2} \\ { (\frac{3}{4}) }^{4} \times ( \frac{4}{3}) ^{10} = ( \frac{4}{3} )^{k + 2} \\ { (\frac{4}{3}) }^{ - 4} \times ( \frac{4}{3}) ^{10} = ( \frac{4}{3} )^{k + 2} \\ ( \frac{4}{3} )^{ - 4 + 10} = ( \frac{4}{3} )^{k + 2} \\ ( \frac{4}{3} )^{6} = ( \frac{4}{3} )^{k + 2}$

So,

$k + 2 = 6 \\ k = 6 - 2 \\ k = 4$

Here applied formulas are

${x}^{a} \times {x}^{b} = {x}^{a + b} \\ {x}^{ {y}^{z} } = {x}^{yz} \\ { (\frac{x}{y}) }^{a} = (\frac{y}{x} )^{ - a}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549