The expression $\frac{(a^1 \times b^7 \times c^7)}{(a^1 \times... | Mathematics MCQ | Examoogle

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The expression $\frac{(a^1 \times b^7 \times c^7)}{(a^1 \times b^2 \times c^{10})}$ in simplified form is:

$(a^2) \times (b^4) \times (c^{-5})$

$(a^0) \times (b^5) \times (c^{-3})$

$(a^4) \times (b^2) \times (c^2)$

$(a^{-8}) \times (b^{-5}) \times (c^{-9})$

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

$(a^0) \times (b^5) \times (c^{-3})$

Quick Summary:

Subtract the exponent in the denominator from the exponent in the numerator for each base: $a^{1-1} b^{7-2} c^{7-10}$ . Any number to the power of 0 is 1.

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📐MAMath SolutionDirect Formula

📋 Given

The expression to simplify is (a¹ * b⁷ * c⁷) / (a¹ * b² * c¹⁰).

🔢 Formula Used

am×bn×cpam×bq×cr=am−m×bn−q×cp−r\frac{a^m \times b^n \times c^p}{a^m \times b^q \times c^r} = a^{m-m} \times b^{n-q} \times c^{p-r}am×bq×cram×bn×cp​=am−m×bn−q×cp−r

⚡ Exam Hall Shortcut / Speed Trick

Subtract the exponent in the denominator from the exponent in the numerator for each base: $a^{1-1} b^{7-2} c^{7-10}$ . Any number to the power of 0 is 1.

⚠️ Common Student Trap / Pitfall

Students often confuse the subtraction of exponents, especially when the exponent in the denominator is larger, leading to negative exponents (e.g., $c^{7-10} = c^{-3}$ ), and forgetting that $a^0 = 1$ .

🔢 Step-by-Step Solution

Group the bases

Write the expression as a product of individual fractions for each base: $\left(\frac{a^1}{a^1}\right) \times \left(\frac{b^7}{b^2}\right) \times \left(\frac{c^7}{c^{10}}\right)$

a1a1×b7b2×c7c10\frac{a^1}{a^1} \times \frac{b^7}{b^2} \times \frac{c^7}{c^{10}}a1a1​×b2b7​×c10c7​

Apply exponent laws

Use the division law for exponents: $x^m / x^n = x^{m-n}$ . Calculate $a^{1-1} = a^0$ , $b^{7-2} = b^5$ , and $c^{7-10} = c^{-3}$ .

a1−1×b7−2×c7−10=a0×b5×c−3a^{1-1} \times b^{7-2} \times c^{7-10} = a^0 \times b^5 \times c^{-3}a1−1×b7−2×c7−10=a0×b5×c−3

Final simplification

Since $a^0 = 1$ , the expression simplifies to $1 \times b^5 \times c^{-3}$ , which is $(a^0) \times (b^5) \times (c^{-3})$ .

(a0)×(b5)×(c−3)(a^0) \times (b^5) \times (c^{-3})(a0)×(b5)×(c−3)

✅

B is correct because the application of exponent laws $\frac{x^m}{x^n} = x^{m-n}$ results in $a^0 \times b^5 \times c^{-3}$ .

Core Concepts Used

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Exponent Laws Base-Exponent Rules Zero Exponent Property

💡 EXAM TIP

This concept is fundamental to solving problems in simplification (VBODMAS), algebraic equations, and scientific notation in physics calculations.

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