plz solve this if u know plz

[tex] {64}^{ - \frac{1}{3} } ( {64}^{ \frac{1}{3} } - {64}^{ \frac{2}{3} } ) \\ {64}^{ \frac{1}{3} - \frac{1}{3} } - {64}^{ \frac{2}{3} - \frac{1}{3} } \\ {64}^{0} - {64}^{ \frac{1}{3} } \\ 1 - \sqrt[3]{64} \\ 1 - 4 \\ - 3[/tex]
[tex] - 3[/tex]
Answer:
- 3
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Thus
[tex]64^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{64}[/tex] = 4
[tex]64^{-\frac{1}{3} }[/tex] = [tex]\frac{1}{4}[/tex]
[tex]64^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{64^{2} }[/tex] = 4² = 16
Substituting values into the given expression
[tex]\frac{1}{4}[/tex] (4 - 16)
= [tex]\frac{1}{4}[/tex] × - 12
= - 3