Explanation

When a power is raised to another power, we multiply exponents:

(m¹⁄₃)³⁄₅ = m^(1/3 × 3/5) = m¹⁄₅

(n⁻²)³⁄₅ = n^(-2 × 3/5) = n⁻⁶⁄₅

So the simplified form is m¹⁄₅ n⁻⁶⁄₅.

Last verified on 24-06-2026

Explanation

Let width = w cm  

Then length = w + 6 cm  

Perimeter of rectangle = 2(length + width)  

2(w + 6 + w) = 48  

2(2w + 6) = 48  

4w + 12 = 48  

4w = 36  

w = 9 cm  

So width = 9 cm, length = 9 + 6 = 15 cm.

Last verified on 23-06-2026

Explanation

For quadratic ax² + bx + c = 0:  

Sum of roots = -b/a  

Product of roots = c/a  

Take a = 1, then:  

-b = sum = -2 → b = 2  

c = product = 3  

So equation: x² + 2x + 3 = 0

Last verified on 23-06-2026

Explanation

Inverse proportion: y ∝ 1/x, so y × x = constant

Given: 10 × 2 = 20

So when x = 5 ⇒ y = 20 ÷ 5 = 4

Last verified on 23-06-2026

Explanation

Diameter = 12 cm ⇒ Radius = 6 cm

Formula: Surface area = 4πr²

= 4π × (6)² = 4π × 36 = 144π cm²

Last verified on 23-06-2026

Explanation

Let the 3-digit number be abc = 100a + 10b + c  

Reversed = cba = 100c + 10b + a  

Given: reversed - original = 297  

(100c + 10b + a) - (100a + 10b + c) = 297  

99c - 99a = 297 → 99(c - a) = 297 → c - a = 3  

Also given: a + c = 7  

Solve:  

a + c = 7  

c - a = 3  

Add both: 2c = 10 → c = 5  

Then a = 7 - 5 = 2  

Product of first and third digits = a × c = 2 × 5 = 10.

Last verified on 23-06-2026

Explanation

Use identity: (a + 1)(a - 1) = a² - 1  

Here 201 × 199 = (200 + 1)(200 - 1) = 200² - 1²  

= 40000 - 1  

= 39999  

Last verified on 23-06-2026

Explanation

2x² + 5x − 12 = 0

Factor form: (2x − 3)(x + 4) = 0

So, x = 3/2 or x = −4

Last verified on 22-06-2026

Explanation

(100)¹·⁵ = (100)³/² = √(100³) 

100³ = 1,000,000  

√1,000,000 = 1000

Last verified on 22-06-2026

Explanation

Diameter = 8 cm → radius r = 8 ÷ 2 = 4 cm  

Height = half of radius → h = 4 ÷ 2 = 2 cm  

Volume = πr²h = π × 4² × 2 = π × 16 × 2 = 32π cm³

Last verified on 21-06-2026