Question

Find the value of n 5^10 ÷ 5^8=(1/5)^n

Answer 1

Answer:

5^10 / 5^8 = 5^2 = 25 so the equation becomes 25 = (1/5) ^ n. This means that n = -2.

Answer 2

Answer:

$n=-2$

Step-by-step explanation:

$\frac{5^{10}}{5^8}=(\frac{1}{5})^n$

Use the law of exponents.

$5^{10-8}=\left(\frac{1}{5}\right)^n$

1/5 can be written with a base of 5.

$5^{10-8}=\left(5^{-1}\right)^n$

Cancel the base 5 on both sides.

$10-8=-1\times \:n$

$2=-n$

Multiply both sides with -1.

$n=-2$