Question
8. \( \frac{7\left(x^{4}\right)^{3}}{\left(3 x^{2}\right)^{2}} \)
Ask by Mejia Stuart. in the Philippines
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \( \frac{7x^{8}}{9} \).
Solution
Calculate or simplify the expression \( \frac{7(x^4)^3}{(3x^2)^2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{7\left(x^{4}\right)^{3}}{\left(3x^{2}\right)^{2}}\)
- step1: Multiply the exponents:
\(\frac{7x^{4\times 3}}{\left(3x^{2}\right)^{2}}\)
- step2: Multiply the numbers:
\(\frac{7x^{12}}{\left(3x^{2}\right)^{2}}\)
- step3: Factor the expression:
\(\frac{7x^{12}}{9x^{4}}\)
- step4: Reduce the fraction:
\(\frac{7x^{8}}{9}\)
The simplified form of the expression \( \frac{7\left(x^{4}\right)^{3}}{\left(3 x^{2}\right)^{2}} \) is \( \frac{7x^{8}}{9} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{7\left(x^{4}\right)^{3}}{\left(3 x^{2}\right)^{2}} \), we'll start with the numerator and denominator separately. In the numerator, we have \( 7\left(x^{4}\right)^{3} = 7x^{12} \) (because \( (x^4)^3 = x^{4 \cdot 3} = x^{12} \)). In the denominator, we compute \( (3x^{2})^{2} = 9x^{4} \) (since \( (3)^2 = 9 \) and \( (x^{2})^2 = x^{4} \)). Now, substituting back, we get: \[ \frac{7x^{12}}{9x^{4}} \] Next, we can simplify this by dividing the coefficients and subtracting the exponents: \[ \frac{7}{9} x^{12 - 4} = \frac{7}{9} x^{8} \] So, the simplified expression is: \[ \frac{7}{9} x^{8} \] And there you have it, simplified and ready to go!
