Let's simplify the expression [tex]\(\frac{x \times \sqrt[3]{x}}{x^{-3}}\)[/tex] step by step.
1. Understand the components of the expression:
- The numerator is [tex]\( x \times \sqrt[3]{x} \)[/tex].
- The denominator is [tex]\( x^{-3} \)[/tex].
2. Simplify the numerator:
- The term [tex]\( \sqrt[3]{x} \)[/tex] can be written as [tex]\( x^{1/3} \)[/tex].
- Thus, the numerator [tex]\( x \times \sqrt[3]{x} \)[/tex] becomes [tex]\( x \times x^{1/3} \)[/tex].
3. Combine powers in the numerator:
- When multiplying terms with the same base, you add the exponents: [tex]\( x \times x^{1/3} = x^{1 + 1/3} = x^{4/3} \)[/tex].
- Therefore, the numerator simplifies to [tex]\( x^{4/3} \)[/tex].
4. Simplify the entire fraction:
- Now we have the fraction [tex]\(\frac{x^{4/3}}{x^{-3}}\)[/tex].
- When dividing terms with the same base, you subtract the exponents: [tex]\( x^{4/3} \div x^{-3} = x^{4/3 - (-3)} = x^{4/3 + 3} \)[/tex].
5. Combine the exponents in the denominator subtraction:
- [tex]\( \frac{4}{3} + 3 \)[/tex] can be calculated by converting 3 into a fraction: [tex]\( 3 = \frac{9}{3} \)[/tex].
- So, [tex]\( \frac{4}{3} + \frac{9}{3} = \frac{13}{3} \)[/tex].
6. Final simplified expression:
- Therefore, the entire expression simplifies to [tex]\( x^{13/3} \)[/tex].
In decimal form, [tex]\( \frac{13}{3} \)[/tex] is approximately [tex]\( 4.3333 \)[/tex].
Thus, the given expression [tex]\(\frac{x \times \sqrt[3]{x}}{x^{-3}}\)[/tex] simplifies to [tex]\( x^{4.3333} \)[/tex], or equivalently [tex]\( x^{13/3} \)[/tex].
