Question

Find the value of k

-(4/5)²×(4/5)⁵=(4/5)6k+1​

Answer 1

Answer:

$\frac{-31503}{125000}$

Step-by-step explanation:

    -(4/5)²×(4/5)⁵= (4/5)6k+1​

⇒-(4/5)⁵⁺²= (4/5)6k+1​

⇒-(4/5)⁷ = (4/5)6k+1

⇒(4/5)6k+1 = -(4/5)⁷

⇒(4/5)6k+1 = -(16384/78125)

⇒(4/5)6k = -(16384/78125)-1

⇒(4/5)6k = $\frac{-16384-78125}{78125}$

⇒(4/5)6k = $\frac{-94509\\}{78125}$

⇒6k = $\frac{-94509\\}{78125}$ ×$\frac{5}{4}$

⇒k =  $\frac{-94509\\}{78125}$×$\frac{5}{4}$×$\frac{1}{6}$

∴k = $\frac{-31503}{125000}$

Answer 2

Answer:

−31503

Step-by-step explanation:

-(4/5)²×(4/5)⁵= (4/5)6k+1

⇒-(4/5)⁵⁺²= (4/5)6k+1

⇒-(4/5)⁷ = (4/5)6k+1

⇒(4/5)6k+1 = -(4/5)⁷

⇒(4/5)6k+1 = -(16384/78125)

⇒(4/5)6k = -(16384/78125)-1

⇒(4/5)6k = \frac{-16384-78125}{78125}

78125

−16384−78125

⇒(4/5)6k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

⇒6k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

×\frac{5}{4}

4

5

⇒k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

×\frac{5}{4}

4

5

×\frac{1}{6}

6

1

∴k = \frac{-31503}{125000}

125000−31503

Step-by-step explanation:

-(4/5)²×(4/5)⁵= (4/5)6k+1

⇒-(4/5)⁵⁺²= (4/5)6k+1

⇒-(4/5)⁷ = (4/5)6k+1

⇒(4/5)6k+1 = -(4/5)⁷

⇒(4/5)6k+1 = -(16384/78125)

⇒(4/5)6k = -(16384/78125)-1

⇒(4/5)6k = \frac{-16384-78125}{78125}

78125

−16384−78125

⇒(4/5)6k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

⇒6k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

×\frac{5}{4}

4

5

⇒k = \begin{gathered}\frac{-94509\\}{78125}\end{gathered}

78125

−94509

×\frac{5}{4}

4

5

×\frac{1}{6}

6

1

∴k = \frac{-31503}{125000}

125000

−31503

−31503