Apply the quotient rule for exponents, which states (a^m)/(aⁿ) = a^m-n.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: Simplify $\frac{k^8}{k^6}$

Apply the quotient rule for exponents, which states $\frac{a^m}{a^n} = a^{m-n}$ .
$k^{8-6}$
Subtract the exponents.
$k^2$
The simplified expression is:
$\boxed{k^2}$
: Simplify $\frac{(4^0)^4}{4^8}$
Simplify the term inside the parenthesis using the zero exponent rule, which states $a^0 = 1$ .
$4^0 = 1$
The expression becomes:
$\frac{(1)^4}{4^8}$
Simplify the numerator.
$(1)^4 = 1$
The expression becomes:
$\frac{1}{4^8}$
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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