(0.04)2 ÷ (0.008) × (0.2)6 = (0.2)?
A. 5
B. 6
C. 8
D. 9
E. None of these
Answer: Option E
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let }}{\left( {0.04} \right)^2} \div \left( {0.008} \right) \times {\left( {0.2} \right)^6} = {\left( {0.2} \right)^x} \cr & {\text{Then,}}{\left( {0.2} \right)^x} = {\left[ {{{\left( {0.2} \right)}^2}} \right]^2} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^{\left( {2 \times 2} \right)}} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^4} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^{\left( {4 - 3 + 6} \right)}} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^7} \cr & \Leftrightarrow x = 7 \cr} $$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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