which expressions are equivalent to $\frac{10}{10^{\frac{3}{4}}}$?

$10^{\frac{4}{3}}$
$10^{\frac{1}{4}}$
$\sqrt3{10^4}$
x $\sqrt4{10}$

Question

which expressions are equivalent to $\frac{10}{10^{\frac{3}{4}}}$?

$10^{\frac{4}{3}}$
  $10^{\frac{1}{4}}$
  $\sqrt3{10^4}$
x $\sqrt4{10}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Radical to Exponential Form" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Radical to Exponential Form" ] } ## Simplify the given expression Using the *Exponent Rules* knowledge point $$ \frac{10}{10^{\frac{3}{4}}} = \frac{10^1}{10^{\frac{3}{4}}} = 10^{1 - \frac{3}{4}} = 10^{\frac{1}{4}} $$ ## Convert to radical form Using the *Radical to Exponential Form* knowledge point $$ 10^{\frac{1}{4}} = \sqrt[4]{10} $$ ## Evaluate the given options Using the *Exponent Rules* and *Radical to Exponential Form* knowledge points $$ \begin{aligned} &\text{Option 1: } 10^{\frac{4}{3}} eq 10^{\frac{1}{4}}\ &\text{Option 2: } 10^{\frac{1}{4}} = 10^{\frac{1}{4}}\ &\text{Option 3: } \sqrt[3]{10^4} = 10^{\frac{4}{3}} eq 10^{\frac{1}{4}}\ &\text{Option 4: } \sqrt[4]{10} = 10^{\frac{1}{4}} \end{aligned} $$

(A) $10^{\frac{4}{3}}$

(B) $10^{\frac{1}{4}}$

(C) $\sqrt[3]{10^4}$

(D) $\sqrt[4]{10}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the given expression

Convert to radical form

Evaluate the given options

Answer: