For any number a and positive integer n, an =a × a × a × ⋯× a (n times)
⭐ 5 Solved Examples of Indices (With Explanation)
(32)3 = 32×3 = 36 = 729
Negative power: 7-2 = 1/72 = 1/49
Fractional power means square root: 161/2 =√16
Q.1. What is 30 ?
📝Explanation: Any non-zero number raised to the power 0 equals 1. This follows from the quotient rule am/am = a0 = 1
Q.2. Simplify 24 × 23 ?
📝 Description:
Same base → add powers:
24+3 = 27 = 128
Q.3. Simplify 75 / 73 ?
📝 Description:
Subtract powers:
75-3 = 72 = 49
Q.4. Evaluate (42)3 ?
📝 Description:
Power of a power rule:
(42)3 = 46 = 4096
Q.5. Value of 10–3 ?
📝 Description:
Negative index = reciprocal:
10-3 = 1/1000 = 0.00110
Q.6. Simplify 91/2 ?
📝 Description:
2√7 + 5√7 = (2+5)√7 = 7√7
Q.7. Value of (23 × 22) ?
📝 Description:
Add powers → 23+2 = 25 = 32.
Q.8. Simplify 54 ÷ 5 ?
📝 Description:
5 = 51.
So 54-1 = 53 = 125
Q.9. Simplify (3×2)3?
📝 Description:
.
Power distributes over product.
Q.10. What is 82/3?
📝 Description:
.
Q.11. Evaluate 321/5?
📝 Description:
Q.12. Solve 2-3/2-1?
📝 Description:
Subtract exponents:
2-3-(-1)= 2-2 = 1/4
But that contradicts options; correction: Should match options → actual:
2-3/ 2-1= 2-2 =1/4
Q.13. Solve (34×3-2)?
📝 Description:
.
Q.14. Value of 49-1/2?
📝 Description:
49-1/2 = 1/√49 = 1/7
Q.15. Solve 64 ÷ 66?
📝 Description:
64-6 = 6-2 = 1/62 = 1/36
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