which expression is equivalent to $(5e^{x})^{3}$?\na) $125e^{3x}$\nb) $125e^{x^{3}}$\nc) $5e^{3x}$\nd)…
which expression is equivalent to $(5e^{x})^{3}$?\na) $125e^{3x}$\nb) $125e^{x^{3}}$\nc) $5e^{3x}$\nd) $5e^{x^{3}}$
Answer
Explanation:
Step1: Apply exponent product rule
$(ab)^n = a^n b^n$, so $(5e^x)^3 = 5^3 \cdot (e^x)^3$
Step2: Calculate $5^3$
$5^3 = 5 \times 5 \times 5 = 125$
Step3: Apply exponent power rule
$(a^m)^n = a^{m \cdot n}$, so $(e^x)^3 = e^{x \cdot 3} = e^{3x}$
Step4: Combine results
Multiply the two simplified terms: $125 \cdot e^{3x}$
Answer:
A) $125e^{3x}$