Question

$(-11)^x\cdot (-11)^4 = \frac{(-11)^{10}}{(-11)^3}$

Explanation:

Step1: Simplify right-hand side

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$
$\frac{(-11)^{10}}{(-11)^3}=(-11)^{10-3}=(-11)^7$

Step2: Simplify left-hand side

Use exponent rule $a^m \cdot a^n=a^{m+n}$
$(-11)^x \cdot (-11)^4=(-11)^{x+4}$

Step3: Equate exponents (same base)

Set exponents equal: $x+4=7$

Step4: Solve for x

Subtract 4 from both sides: $x=7-4$

Answer:

$x=3$