Surds and Indices Quiz Set 007

We can write the given expression as $3^x = 3^6$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get $3^5 = 243$.

We can simplify the given expression to $({27/28})^{2x - 1.5} = ({27/28})^0.29$. The bases are equal, so the powers should also be equal. Hence $2x - 1.5 = 0.29$ which gives x = 0.895.

By inspection, we get $(2^12)^0.15 × (2^12)^0.1$, which equals $(2^12)^(0.15 + 0.1)$, which equals $(2^12)^0.25$, which equals $2^3$, or 8. Note: The trick in such type of questions is to keep an eye on the "bases".

Simplifying, we get $7^{364 - 360}$ which equals$7^4$, or 2401.

We can simplify the given expression to $({5/23})^{0.05 + x} = ({5/23})^3.2$. The bases are equal, so the powers should also be equal. Hence $0.05 + x = 3.2$ which gives x = 3.15.