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If x is different from zero and x^2x^4(x^2)^3
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26 Sep 2025, 00:53
26 Sep 2025, 00:53
Expert Reply
00:00
Question Stats:
92% (00:26) correct
7% (01:05) wrong based on 14 sessions
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If \(x \neq 0\), then \(\frac{\left[x^2 x^4\left(x^2\right)^3\right]}{x^4}\)
(A) \(x\)
(B) \(x^2\)
(C) \(x^7\)
(D) \(x^8\)
(E) \(x^{12}\)
(A) \(x\)
(B) \(x^2\)
(C) \(x^7\)
(D) \(x^8\)
(E) \(x^{12}\)
- Part of the project: PrepClub Daily GRE Quant Questions: Arithmetic, Algebra, Geometry & DA
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Re: If x is different from zero and x^2x^4(x^2)^3
[#permalink]
16 Oct 2025, 13:05
16 Oct 2025, 13:05
Expert Reply
Let's simplify the expression step-by-step:
$$
\(\frac{\left[x^2 \cdot x^4 \cdot\left(x^2\right)^3\right]}{x^4}\)
$$
1. Simplify inside the numerator by using exponent rules:
$$
\(x^2 \cdot x^4=x^{2+4}=x^6\)
$$
2. Simplify power of power:
$$
\(\left(x^2\right)^3=x^{2 \times 3}=x^6\)
$$
3. Multiply all numerator terms:
$$
\(x^6 \cdot x^6=x^{6+6}=x^{12}\)
$$
4. Now divide by denominator $\(x^4\)$ :
$$
\(\frac{x^{12}}{x^4}=x^{12-4}=x^8\)
$$
$$
\(\frac{\left[x^2 \cdot x^4 \cdot\left(x^2\right)^3\right]}{x^4}\)
$$
1. Simplify inside the numerator by using exponent rules:
$$
\(x^2 \cdot x^4=x^{2+4}=x^6\)
$$
2. Simplify power of power:
$$
\(\left(x^2\right)^3=x^{2 \times 3}=x^6\)
$$
3. Multiply all numerator terms:
$$
\(x^6 \cdot x^6=x^{6+6}=x^{12}\)
$$
4. Now divide by denominator $\(x^4\)$ :
$$
\(\frac{x^{12}}{x^4}=x^{12-4}=x^8\)
$$
gmatclubot
Re: If x is different from zero and x^2x^4(x^2)^3 [#permalink]
16 Oct 2025, 13:05
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