Hasil dari (81x3yz2/27x2y4z2)4 adalah ....

Question

ScanSolve AI Tutor · Accepted Answer

To simplify the expression, we will first simplify the fraction inside the parentheses and then raise the entire result to the power of 4.

Simplify the numerical coefficients.
$\frac{81}{27} = 3$
Simplify the terms with $x$ using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$x^{\frac{3}{4} - \frac{1}{2}} = x^{\frac{3}{4} - \frac{2}{4}} = x^{\frac{1}{4}}$
Simplify the terms with $y$ using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
The exponent of $y$ in the numerator is 1.
$y^{1 - \frac{1}{4}} = y^{\frac{4}{4} - \frac{1}{4}} = y^{\frac{3}{4}}$
Simplify the terms with $z$ using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$z^{\frac{3}{2} - \frac{1}{2}} = z^{\frac{2}{2}} = z^1 = z$
Combine the simplified terms inside the parentheses.
$\left( 3x^{\frac{1}{4}}y^{\frac{3}{4}}z \right)^4$
Apply the outer exponent of 4 to each term inside the parentheses using the rule $(abc)^n = a^n b^n c^n$ and $(a^m)^n = a^{mn}$ .
$3^4 \left(x^{\frac{1}{4}}\right)^4 \left(y^{\frac{3}{4}}\right)^4 (z)^4$ $81 x^{\frac{1}{4} \times 4} y^{\frac{3}{4} \times 4} z^4$ $81 x^1 y^3 z^4$ $81xy^3z^4$
The simplified expression is $81xy^3z^4$ . This matches option D.

The final answer is $\text{D. } 81xy^3z^4$ .

Hasil dari ((81x3yz2)/(27x2y4z2))4 adalah ....