Question
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Tutor-Verified Answer
Answer
\( x^{13} \)
Solution
Calculate or simplify the expression \( (x^5)^3 / x^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x^{5}\right)^{3}}{x^{2}}\)
- step1: Multiply the exponents:
\(\frac{x^{5\times 3}}{x^{2}}\)
- step2: Multiply the numbers:
\(\frac{x^{15}}{x^{2}}\)
- step3: Reduce the fraction:
\(\frac{x^{15-2}}{1}\)
- step4: Simplify:
\(x^{15-2}\)
- step5: Divide the terms:
\(x^{13}\)
The simplified form of \( \left(x^{5}\right)^{3} \div x^{2} \) is \( x^{13} \).
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Simplify this solution Mind Expander
To simplify \( \left(x^{5}\right)^{3} \div x^{2} \), start by applying the power of a power rule: \( (a^m)^n = a^{m \cdot n} \). This gives us \( x^{15} \) from \( (x^5)^3 \). Now, divide by \( x^2 \) using the quotient rule: \( a^m \div a^n = a^{m-n} \). This results in \( x^{15-2} = x^{13} \). So, the simplified expression is \( x^{13} \).
