Apply the quotient rule for exponents, which states (a^m)/(a^n) = a^m-n.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems:
Problem 1: Simplify $\frac{k^8}{k^6}$
Step 1: Apply the quotient rule for exponents, which states $\frac{a^m}{a^n} = a^{m-n}$.
$$ k^{8-6} $$
Step 2: Subtract the exponents.
$$ k^2 $$
The simplified expression is:
$$\boxed{k^2}$$
Problem 2: Simplify $\frac{(4^0)^4}{4^8}$
Step 1: Simplify the term inside the parenthesis using the zero exponent rule, which states $a^0 = 1$.
$$ 4^0 = 1 $$
The expression becomes:
$$ \frac{(1)^4}{4^8} $$
Step 2: Simplify the numerator.
$$ (1)^4 = 1 $$
The expression becomes:
$$ \frac{1}{4^8} $$
Step 3: Rewrite the expression using a negative exponent, which states $\frac{1}{a^n} = a^{-n}$.
$$ 4^{-8} $$
The simplified expression is:
$$\boxed{4^{-8}}$$
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