The expression $\frac{(a^5 imes b^9 imes c^1)}{(a^6 imes b^3 imes c^8)}$ in simplified form is:

Question

The expression $\frac{(a^5 	imes b^9 	imes c^1)}{(a^6 	imes b^3 	imes c^8)}$ in simplified form is:

Examoogle · Accepted Answer

The correct answer is Option D: $(a^{-1}) 	imes (b^6) 	imes (c^{-7})$. Subtract the exponent of the denominator from the exponent of the numerator for each base: a: 5-6 = -1; b: 9-3 = 6; c: 1-8 = -7.

Step-by-Step Solution & Concepts:
Shortcut Trick: Subtract the exponent of the denominator from the exponent of the numerator for each base: a: 5-6 = -1; b: 9-3 = 6; c: 1-8 = -7.

Formula Used: $$\frac{x^m}{x^n} = x^{m-n}$$

Given: Expression to simplify: (a^5 × b^9 × c^1) / (a^6 × b^3 × c^8)

Steps: Group terms by base: To simplify, rewrite the expression by grouping terms with the same base $a$, $b$, and $c$.. Apply exponent rule: Use the quotient rule for exponents: $\frac{x^m}{x^n} = x^{m-n}$. Apply this to each base.. Calculate final exponents: Perform the subtraction for each variable: $5-6 = -1$, $9-3 = 6$, and $1-8 = -7$.

Answer: D is correct because applying the quotient rule for exponents $\frac{x^m}{x^n} = x^{m-n}$ to the given expression yields $a^{-1} 	imes b^6 	imes c^{-7}$.

Exam Tip: This concept is foundational for scientific notation and calculus (differentiation of polynomials), where you frequently move between denominators and negative exponents.

Examoogle · Answer

Option A: $(a^4) 	imes (b^{-10}) 	imes (c^1)$

Examoogle · Answer

Option B: $(a^{-10}) 	imes (b^{-5}) 	imes (c^{-8})$

Examoogle · Answer

Option C: $(a^{-5}) 	imes (b^3) 	imes (c^{-6})$

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)