Pregunta
e. \( \left(\frac{5^{x}}{2}\right)^{2} \quad \) f. \( 9^{2 x} \div 9^{x} \)
Ask by Vargas Chan. in South Africa
Feb 13,2025
Solución de inteligencia artificial de Upstudy
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e. \( \frac{5^{2x}}{4} \)
f. \( 9^{x} \)
Solución
Let's simplify each expression step by step.
e. Simplify ( (5ˣ) / 2 )²:
• First, apply the exponent 2 to both the numerator and the denominator:
(5ˣ / 2)² = (5ˣ)² / 2².
• Next, simplify each part:
(5ˣ)² = 5^(2x) and 2² = 4.
• Therefore, the simplified expression is:
5^(2x) / 4.
f. Simplify 9^(2x) ÷ 9ˣ:
• Use the property of exponents which states that when dividing like bases, subtract the exponents:
9^(2x) ÷ 9ˣ = 9^(2x - x) = 9^(x).
So, the final simplified expressions are:
e. 5^(2x) / 4
f. 9^(x)
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Simplifique esta solución Beyond the Answer
Let's break down each expression to make it fun and easy! In the first expression, \( \left(\frac{5^{x}}{2}\right)^{2} \) can be expanded to \( \frac{(5^{x})^{2}}{2^{2}} \), which simplifies to \( \frac{25^{x}}{4} \). It’s like bringing a little magic by transforming the fraction into a neat power! For the second expression, \( 9^{2x} \div 9^{x} \) can be simplified using the law of exponents, \( a^{m} \div a^{n} = a^{m-n} \). So, we get \( 9^{2x-x} = 9^{x} \). Voilà! Simple division turns into an elegant expression, showcasing how easily exponents play together.
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