Question

1024^{-2} = 16^{x+3}

Explanation:

Step1: Rewrite with base 2

$1024=2^{10}$, $16=2^4$, so:
$$(2^{10})^{-2}=(2^4)^{x+3}$$

Step2: Simplify exponents

Use $(a^m)^n=a^{m \cdot n}$:
$$2^{-20}=2^{4(x+3)}$$

Step3: Set exponents equal

If $a^m=a^n$ ($a>0,a
eq1$), $m=n$:
$$-20=4(x+3)$$

Step4: Solve for x

Divide by 4, then subtract 3:
$$-5=x+3 \implies x=-5-3$$

Answer:

$x=-8$