Question

question 9
simplify the expression.
(enter your answer as a whole number or fraction)
$4^2 \cdot 4^{-4} = $
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question 10
simplify the expression.
$(1)^2 = $
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Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$.
$4^2 \cdot 4^{-4} = 4^{2 + (-4)} = 4^{-2}$

Step2: Rewrite negative exponent as fraction

A negative exponent means reciprocal: $a^{-n} = \frac{1}{a^n}$.
$4^{-2} = \frac{1}{4^2} = \frac{1}{16}$

Step3: Simplify the squared term

Any number squared is itself multiplied by itself.
$(1)^2 = 1 \times 1 = 1$

Answer:

$4^2 \cdot 4^{-4} = \frac{1}{16}$
$(1)^2 = 1$