The expression $\frac{(a^{10} imes b^3 imes c^9)}{(a^9 imes b^6 imes c^9)}$ in simplified form is:

Question

The expression $\frac{(a^{10} 	imes b^3 	imes c^9)}{(a^9 	imes b^6 	imes c^9)}$ in simplified form is:

Examoogle · Accepted Answer

The correct answer is Option B: $(a^1) 	imes (b^{-3}) 	imes (c^0)$. Use laws of exponents by subtracting the exponents of the denominator from the numerator for each base: $a^{10-9} 	imes b^{3-6} 	imes c^{9-9}$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use laws of exponents by subtracting the exponents of the denominator from the numerator for each base: $a^{10-9} 	imes b^{3-6} 	imes c^{9-9}$.

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

Given: Expression: \frac{(a^{10} 	imes b^3 	imes c^9)}{(a^9 	imes b^6 	imes c^9)}

Steps: Step 1: Write the given expression: We are given the algebraic fraction containing powers of $a$, $b$, and $c$: $$\frac{(a^{10} 	imes b^3 	imes c^9)}{(a^9 	imes b^6 	imes c^9)}$$. Step 2: Apply the law of exponents for division: Using the exponent rule $\frac{x^m}{x^n} = x^{m-n}$, apply it to each base separately: for base $a$, $10-9 = 1$; for base $b$, $3-6 = -3$; for base $c$, $9-9 = 0$.. Step 3: Simplify the powers: Subtracting the exponents yields $(a^1) 	imes (b^{-3}) 	imes (c^0)$.

Answer: C is correct because simplifying the expression using the laws of exponents yields $(a^1) 	imes (b^{-3}) 	imes (c^0)$.

Exam Tip: Understanding exponent rules is crucial not only in algebra but also in simplifying complex algebraic fractions in calculus and physics formulas.

Examoogle · Answer

Option A: $(a^{-1}) 	imes (b^{-3}) 	imes (c^{-10})$

Examoogle · Answer

Option C: $(a^1) 	imes (b^{-9}) 	imes (c^{-7})$

Examoogle · Answer

Option D: $(a^{-1}) 	imes (b^{-9}) 	imes (c^{-8})$

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