Surds and Indices Quiz Set 012

By inspection, both the expressions can be simplified to $4^{m + n} = 4^6$ and $4^{m - n} = 4^3$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 6$ and $m - n = 3$. Solving, we get $m = {6 + 3}/2$ = 4.5. Note: The trick in such type of questions is to keep an eye on the "bases".

By inspection, we get $(3^4)^0.11 × (3^4)^0.14$, which equals $(3^4)^(0.11 + 0.14)$, which equals $(3^4)^0.25$, which equals $3^1$, or 3. Note: The trick in such type of questions is to keep an eye on the "bases".

We can simplify the given expression to $({33/18})^{0.18 + x} = ({33/18})^0.3$. The bases are equal, so the powers should also be equal. Hence $0.18 + x = 0.3$ which gives x = 0.12.

We can write the given expression as $8^x = 8^3$. The bases are same so powers should be same. Comparing we get x = 3.

Simplifying, we get $7^{499 - 496}$ which equals$7^3$, or 343.