evaluate 64^a/6 / 4^a × 2^2a +1 / 2^a-1
Answers
Simplify the following
(2-¹×3²/2²×3‐⁴)⁷/²×(2-²×3³/2³×3-⁵)-⁵/²
(ans 12)
https://brainly.in/question/16527751
Answer:
Solution:
\textsf{Consider,}Consider,
\mathsf{\dfrac{64^\frac{a}{6}}{4^a}{\times}\dfrac{2^{2a+1}}{2^{a-1}}}
4
a
64
6
a
×
2
a−1
2
2a+1
\textsf{This can be written as}This can be written as
\mathsf{=\dfrac{(2^6)^\frac{a}{6}}{(2^2)^a}{\times}\dfrac{2^{2a+1}}{2^{a-1}}}=
(2
2
)
a
(2
6
)
6
a
×
2
a−1
2
2a+1
\mathsf{=\dfrac{2^a}{2^{2a}}{\times}\dfrac{2^{2a+1}}{2^{a-1}}}=
2
2a
2
a
×
2
a−1
2
2a+1
\mathsf{Using,}Using,
\boxed{\mathsf{\dfrac{a^m}{a^n}=a^{m-n}}}
a
n
a
m
=a
m−n
\mathsf{=2^{a-2a}{\times}2^{(2a+1)-(a-1)}}=2
a−2a
×2
(2a+1)−(a−1)
\mathsf{=2^{-a}{\times}2^{2a+1-a+1}}=2
−a
×2
2a+1−a+1
\mathsf{=2^{-a}{\times}2^{a+2}}=2
−a
×2
a+2
\mathsf{Using,}Using,
\boxed{\mathsf{a^m{\times}a^n=a^{m+n}}}
a
m
×a
n
=a
m+n
\mathsf{=2^{-a+a+2}}=2
−a+a+2
\mathsf{=2^{2}}=2
2
\mathsf{=4}=4
\implies\boxed{\mathsf{\dfrac{64^\frac{a}{6}}{4^a}{\times}\dfrac{2^{2a+1}}{2^{a-1}}=4}}⟹
4
a
64
6
a
×
2
a−1
2
2a+1
=4
\textbf{Find more:}Find more:
Simplify the following
(2-¹×3²/2²×3‐⁴)⁷/²×(2-²×3³/2³×3-⁵)-⁵/²
(ans 12)
https://brainly.in/question/16527751