Question

find the value of K
$( \frac{ - 5}{11} ) {}^{k + 2} \div ( \frac{ - 5}{11} ) {}^{ - 4k + 5} = ( \frac{ - 5}{11} {}^{2k}$
​

Answer 1

Since the base numbers are the same, we will apply the exponent power law which is ⇒ $\frac{a^{m}}{a^{n}} =a^{m}\div a^{n} = a^{m-n}$

So here the equation would be ⇒

$(k+2)-(-4k+5)=2k$

Step 1: Simplify both sides of the equation.

$k+2-(-4k+5)=2k$

(Distribute the Negative Sign)

$k+2+-1(-4k+5)=2k$

$k+2+-1(-4k)+(-1)(5)=2k$

$k+2+4k+-5=2k$

(Combine Like Terms)

$(k+4k)+(2+-5)=2k$

$5k+-3=2k$

$5k-3=2k$

Step 2: Subtract 2k from both sides.

$5k-3-2k=2k-2k$

$3k-3=0$

Step 3: Add 3 to both sides.

$3k-3+3=0+3$

$3k=3$

Step 4: Divide both sides by 3.

$\frac{3k}{3}=\frac{3}{3}$

$k=1$

Verification if $k=1$

$(1+2)-((-4\times 1)+5)$

$3-(-4+5)$

$3-1$

$2$

$2\times 1 = 2$

∴ $k=1$ in the equation $(\frac{-5}{11})^{k+2}\div(\frac{-5}{11})^{-4k+5}=(\frac{-5}{11}) ^{2k}$

Additional Information ❤

What is an equation?

A statement that shows the equality of two expressions is known as an equation.

What are the types of equation?

There are five types of equations. They are as follows.

• Polynomial Equation
• Quadratic Equation
• Rational Polynomial Equation
• Trigonometric Equation
• Cubic Equation

Answer 2

Pls mark as brainliest answer