en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (4pi80^2)*(4)

Solution

simplify

(4 \cdot π \cdot 8 0^{2}) \cdot (4)

Solution

102400 π

+1

Decimal Notation

321699.08772 \dots

Solution steps

(4 π 8 0^{2}) (4)

Apply exponent rule:

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

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

= π 8 0^{2} \cdot 4^{1 + 1}

Add the numbers:

1 + 1 = 2

= π 8 0^{2} \cdot 4^{2}

Factor integer

80 = 2^{4} \cdot 5

= π (2^{4} \cdot 5)^{2} \cdot 4^{2}

Apply exponent rule:

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

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

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

Apply exponent rule:

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

(2^{4})^{2} = 2^{4 \cdot 2}

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

Refine

= π 2^{8} \cdot 5^{2} \cdot 4^{2}

Factor integer

4 = 2^{2}

= π 2^{8} \cdot 5^{2} (2^{2})^{2}

Apply exponent rule:

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

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

= π 2^{8} \cdot 5^{2} \cdot 2^{2 \cdot 2}

Refine

= π 2^{8} \cdot 5^{2} \cdot 2^{4}

Apply exponent rule:

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

2^{8} \cdot 2^{4} = 2^{8 + 4}

= π 5^{2} \cdot 2^{8 + 4}

Add the numbers:

8 + 4 = 12

= π 5^{2} \cdot 2^{12}

5^{2} = 25

= 2^{12} \cdot 25 π

2^{12} = 4096

= 25 \cdot 4096 π

Multiply the numbers:

25 \cdot 4096 = 102400

= 102400 π

Popular Examples

simplify (e^{-6x})(-2e^{-2x})simplify

(e^{- 6 x}) (- 2 e^{- 2 x})

simplify (sqrt(85))^2 simplify

(85)^{2}

simplify e^{-ln(2t)}sin(pit)simplify

e^{- l n (2 t)} sin (π t)

simplify e^{-3}(3^2)/(2!)simplify

e^{- 3} \frac{3 ^{2}}{2 !}

simplify (e^{ln(x)})^2 simplify

(e^{l n (x)})^{2}

Frequently Asked Questions (FAQ)

What is (4*pi*80^2)*(4) ?
The solution to (4*pi*80^2)*(4) is 102400pi