Express (5p3​)−2 using positive indices.

Write x−74​ using the radical symbol (​).

Find the value of (0.027)32​.

Find the value of (8116​)−43​.

Simplify: a0b−1(2a)−2×9a4​​

Solve for x: 52x−1=125

Solve for a: 8a−1=(41​)a

Solve for y: (3y​)2=36

Simplify: 2lg5+lg40−lg10

Simplify: loga​12+loga​5−loga​15

Solve for x: log3​x=log3​18−log3​2

Solve for y: logy​81−logy​3=2

Find the value of 2731​×(0.25)−21​.

If 2x×4x−1=32, find the value of x.

Given lg 2=0.3010 and lg 3=0.4771, find the value of lg 12 without using tables.