en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4pi(3*40^24)

Solution

simplify

4 π (3 \cdot 4 0^{2} 4)

Solution

76800 π

+1

Decimal Notation

241274.31579 \dots

Solution steps

4 π (3 \cdot 4 0^{2} \cdot 4)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

4 \cdot 4 = 4^{1 + 1}

= π 3 \cdot 4 0^{2} \cdot 4^{1 + 1}

Add the numbers:

1 + 1 = 2

= π 3 \cdot 4 0^{2} \cdot 4^{2}

Factor integer

40 = 2^{3} \cdot 5

= π 3 (2^{3} \cdot 5)^{2} \cdot 4^{2}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2^{3} \cdot 5)^{2} = (2^{3})^{2} \cdot 5^{2}

= π 3 (2^{3})^{2} \cdot 5^{2} \cdot 4^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{3})^{2} = 2^{3 \cdot 2}

= π 3 \cdot 2^{3 \cdot 2} \cdot 5^{2} \cdot 4^{2}

Refine

= π 3 \cdot 2^{6} \cdot 5^{2} \cdot 4^{2}

Factor integer

4 = 2^{2}

= π 3 \cdot 2^{6} \cdot 5^{2} (2^{2})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{2})^{2} = 2^{2 \cdot 2}

= π 3 \cdot 2^{6} \cdot 5^{2} \cdot 2^{2 \cdot 2}

Refine

= π 3 \cdot 2^{6} \cdot 5^{2} \cdot 2^{4}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{6} \cdot 2^{4} = 2^{6 + 4}

= π 3 \cdot 5^{2} \cdot 2^{6 + 4}

Add the numbers:

6 + 4 = 10

= π 3 \cdot 5^{2} \cdot 2^{10}

5^{2} = 25

= 2^{10} \cdot 3 \cdot 25 π

2^{10} = 1024

= 3 \cdot 25 \cdot 1024 π

Multiply the numbers:

3 \cdot 25 \cdot 1024 = 76800

= 76800 π

Popular Examples

simplify (36e^{-x}cos(2x))(sin(3x))simplify

(36 e^{- x} cos (2 x)) (sin (3 x))

simplify sqrt(((5)^2-(12)^2)^{-1)}simplify

((5)^{2} - (12)^{2})^{- 1}

simplify e^{-0.72*2}simplify

e^{- 0.72 \cdot 2}

simplify e^{-x}(sin(x))simplify

e^{- x} (sin (x))

simplify \sqrt[4]{(-5)}^4 simplify

Frequently Asked Questions (FAQ)

What is 4pi(3*40^24) ?
The solution to 4pi(3*40^24) is 76800pi