what is the value of $b$ in the equation $(y^b)^4 = \frac{1}{y^{24}}$?

-20
-6
6
20

Question

what is the value of $b$ in the equation $(y^b)^4 = \frac{1}{y^{24}}$?

-20
-6
6
20

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Negative Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Simplify the left side of the equation $$ (y^b)^4 = y^{4b} $$ ## Simplify the right side of the equation $$ \frac{1}{y^{24}} = y^{-24} $$ ## Equate exponents and solve for b $$ \begin{aligned} y^{4b} &= y^{-24} \ 4b &= -24 \ b &= -6 \end{aligned} $$

(A) $-20$

(B) $-6$

(C) $6$

(D) $20$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the left side of the equation

Simplify the right side of the equation

Equate exponents and solve for b

Answer: