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Answer :
To simplify the expression
[tex]$$
\frac{6x^3}{3x},
$$[/tex]
we follow these steps:
1. Divide the coefficients.
The coefficients are 6 (numerator) and 3 (denominator). Dividing these gives:
[tex]$$
\frac{6}{3} = 2.
$$[/tex]
2. Divide the powers of [tex]\( x \)[/tex].
The numerator has [tex]\( x^3 \)[/tex] and the denominator has [tex]\( x \)[/tex] (which is [tex]\( x^1 \)[/tex]). When dividing expressions with the same base, subtract the exponents:
[tex]$$
x^3 \div x^1 = x^{3-1} = x^2.
$$[/tex]
3. Combine the results.
Multiply the result from the coefficients by the result from the [tex]\( x \)[/tex] division:
[tex]$$
2 \cdot x^2 = 2x^2.
$$[/tex]
Thus, the simplified expression is:
[tex]$$
2x^2.
$$[/tex]
Among the multiple-choice options given:
1. [tex]\( 9x^4 \)[/tex]
2. [tex]\( 2x^2 \)[/tex]
3. [tex]\( 3x^2 \)[/tex]
4. [tex]\( 18x^4 \)[/tex]
The correct answer is option 2.
[tex]$$
\frac{6x^3}{3x},
$$[/tex]
we follow these steps:
1. Divide the coefficients.
The coefficients are 6 (numerator) and 3 (denominator). Dividing these gives:
[tex]$$
\frac{6}{3} = 2.
$$[/tex]
2. Divide the powers of [tex]\( x \)[/tex].
The numerator has [tex]\( x^3 \)[/tex] and the denominator has [tex]\( x \)[/tex] (which is [tex]\( x^1 \)[/tex]). When dividing expressions with the same base, subtract the exponents:
[tex]$$
x^3 \div x^1 = x^{3-1} = x^2.
$$[/tex]
3. Combine the results.
Multiply the result from the coefficients by the result from the [tex]\( x \)[/tex] division:
[tex]$$
2 \cdot x^2 = 2x^2.
$$[/tex]
Thus, the simplified expression is:
[tex]$$
2x^2.
$$[/tex]
Among the multiple-choice options given:
1. [tex]\( 9x^4 \)[/tex]
2. [tex]\( 2x^2 \)[/tex]
3. [tex]\( 3x^2 \)[/tex]
4. [tex]\( 18x^4 \)[/tex]
The correct answer is option 2.
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