9. Simplify: (64)^-1/3 [(64^1/3) – (64^2/3)]
Answers
Answer:
64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})=-364
−
3
1
(64
3
1
−64
3
2
)=−3
Step-by-step explanation:
Given : Expression 64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})64
−
3
1
(64
3
1
−64
3
2
)
To find : Simplify the expression ?
Solution :
We know that, 64=4^364=4
3
Replace that,
=(4^3)^{-\frac{1}{3}}((4^3)^{\frac{1}{3}}-(4^3)^{\frac{2}{3}})=(4
3
)
−
3
1
((4
3
)
3
1
−(4
3
)
3
2
)
Applying exponent identity, (a^b)^x=a^{b\times x}(a
b
)
x
=a
b×x
=(4)^{-\frac{3}{3}}((4)^{\frac{3}{3}}-(4)^{\frac{2\times 3}{3}})=(4)
−
3
3
((4)
3
3
−(4)
3
2×3
)
=(4)^{-1}((4)^{1}-(4)^{2})=(4)
−1
((4)
1
−(4)
2
)
=(4)^{-1}(4-16)=(4)
−1
(4−16)
=\frac{1}{4}\times(-12)=
4
1
×(−12)
=-3=−3
Therefore, 64^{-\frac{1}{3}}(64^{\frac{1}{3}}-64^{\frac{2}{3}})=-364
−
3
1
(64
3
1
−64
3
2
)=−3
Hello mate....
Hope it helps you.....
