Question

solve for m :
(-5)^m-1÷(-5)^2=(-5)^-8​

Answer 1

Question

Find the value of 'm' in the equation ⇒ $(-5)^{m-1}\div (-5)^{2} = (-5)^{-8}$

$\rule{300}{1}$

Answer

Step 1: Since the bases are same we will take the exponents and solve the equation. Here we should keep this law of exponents in mind ⇒ $a^{m} \div a^{n} = a^{m+n}$

Let's solve your equation step-by-step.

$(m-1)-2=-8$

Step 1: Simplify both sides of the equation.

$m-1-2=-8$

$m+-1+-2=-8$

(Combine Like Terms)

$(m)+(-1+-2)=-8$

$m+-3=-8$

$m-3=-8$

Step 2: Add 3 to both sides.

$m-3+3=-8+3$

$m=-5$

Let's verify if the value of 'm' is (-5)

$(-5)^{m-1}\div (-5)^{2} = (-5)^{-8}$

$(-5)^{-5-1}\div (-5)^{2} = (-5)^{-8}$

$(-5)^{-6}\div (-5)^{2} = (-5)^{-8}$

Apply this law ⇒ $a^{m} \div a^{n} = a^{m-n}$

$(-5)^{-6-2}=(-5)^{-8}$

$(-5)^{-8} = (-5)^{-8}$

∴LHS = RHS

∴ m = -5 in the equation ⇒ $\bf (-5)^{m-1}\div (-5)^{2} = (-5)^{-8}$

$\rule{300}{1}$

Answer 2

Answer:

Answer

Question

Find the value of 'm' in the equation ⇒

Answer

Step 1: Since the bases are same we will take the exponents and solve the equation. Here we should keep this law of exponents in mind ⇒

Let's solve your equation step-by-step.

Step 1: Simplify both sides of the equation.