$${\left( {32 \times {{10}^{ - 5}}} \right)^{ 2}} \times $$ $$64\, \div $$ $$\left( {{2^{16}} \times {{10}^{ - 4}}} \right)$$ $$ = $$ $${10^?}$$
A. 6
B. 10
C. -8
D. -6
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\left( {32 \times {{10}^{ - 5}}} \right)^{ 2}} \times 64 \div \left( {{2^{16}} \times {{10}^{ - 4}}} \right) = {10^?} \cr & \Rightarrow {\left( {{2^5} \times {{10}^{ - 5}}} \right)^{ 2}} \times {2^6} \div \left( {{2^{16}} \times {{10}^{ - 4}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {10^?}.....\left[ {\because {{\left( {{a^m}} \right)}^n} = {a^{mn}}} \right] \cr & \Rightarrow \frac{{{2^{10}} \times {{10}^{ - 10}} \times {2^6}}}{{{2^{16}} \times {{10}^{ - 4}}}} \cr & \,\,\,\,\,\,\,\,\,\, = {10^?}.....\left[ {\because {a^m} \times {a^n} = {a^{m + n}}} \right] \cr & \Rightarrow \frac{{{2^{16}} \times {{10}^4}}}{{{2^{16}} \times {{10}^{10}}}} \cr & \,\,\,\,\,\,\,\, = {10^?}.....\left[ {{a^{ - m}} = \frac{1}{{{a^m}}}} \right] \cr & \Rightarrow {10^{4 - 10}} = {10^?} \cr & \Rightarrow {10^{ - 6}} = {10^?} \cr & \Rightarrow ? = - 6 \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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