Question

question 11
simplify the expression. enter your answer as a whole number or fraction.
$4^{-2} \div 4^2 = \square$
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question 12
simplify the given expression. write the answer with positive exponents only.
$(xy^4)^3 \frac{1}{x^4y^3} = \square$
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Explanation:

Step1: Use exponent division rule

For same bases, $a^m \div a^n = a^{m-n}$
$4^{-2} \div 4^2 = 4^{-2-2}$

Step2: Calculate exponent value

$4^{-4}$

Step3: Convert to positive exponent

$4^{-4} = \frac{1}{4^4}$

Step4: Compute denominator

$4^4 = 256$, so $\frac{1}{256}$

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Step1: Expand the power term

$(xy^4)^3 = x^3(y^4)^3 = x^3y^{12}$

Step2: Multiply with the fraction

$x^3y^{12} \cdot \frac{1}{x^4y^3} = \frac{x^3y^{12}}{x^4y^3}$

Step3: Apply exponent division rule

For $x$: $x^{3-4}=x^{-1}$; For $y$: $y^{12-3}=y^9$
$\frac{x^{-1}y^9}{1}$

Step4: Convert to positive exponents

$x^{-1} = \frac{1}{x}$, so $\frac{y^9}{x}$

Answer:

Question 11: $\frac{1}{256}$
Question 12: $\frac{y^9}{x}$