Surds and Indices Quiz Set 001

By inspection we can see that p = 5, q= 2. So $(5 - 1)^(2 + 1)$ will be $4^3$, i.e., 64.

We can write the given expression as $6^x = 6^2$. The bases are same so powers should be same. Comparing we get x = 2.

Substituting in $p^m = q^4$, we get $34^{0.21m} = 34^{0.22 × 4}$. Bases are same so powers should be same. Hence, $0.21m = {0.22 × 4}$, which gives m = 4.19.

By inspection we can see that p = 8, q= 3. So $(8 - 1)^(3 + 1)$ will be $7^4$, i.e., 2401.

Simplifying, we get $(5^2)^1.5 × 5^9$ ÷ $(5 ^ 4)^3$ = $5^x$, which simplifies to $5^3 × 5^9$ ÷ $5^12$ = $5^x.$ Equating the powers x = 3 + 9 - 12 = 0.