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Popular >

simplify 4*10^{20}(4pi)

Solution

simplify

4 \cdot 1 0^{20} (4 π)

Solution

5^{20} \cdot 16777216 π

+1

Decimal Notation

5.02655 E 21

Solution steps

4 \cdot 1 0^{20} (4 π)

Apply exponent rule:

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

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

= 1 0^{20} \cdot 4^{1 + 1} π

Add the numbers:

1 + 1 = 2

= 1 0^{20} \cdot 4^{2} π

Factor integer

10 = 2 \cdot 5

= (2 \cdot 5)^{20} \cdot 4^{2} π

Apply exponent rule:

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

(2 \cdot 5)^{20} = 2^{20} \cdot 5^{20}

= 2^{20} \cdot 5^{20} \cdot 4^{2} π

Factor integer

4 = 2^{2}

= 2^{20} \cdot 5^{20} (2^{2})^{2} π

Apply exponent rule:

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

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

= 2^{20} \cdot 5^{20} \cdot 2^{2 \cdot 2} π

Refine

= 2^{20} \cdot 5^{20} \cdot 2^{4} π

Apply exponent rule:

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

2^{20} \cdot 2^{4} = 2^{20 + 4}

= 5^{20} \cdot 2^{20 + 4} π

Add the numbers:

20 + 4 = 24

= 5^{20} \cdot 2^{24} π

2^{24} = 16777216

= 5^{20} \cdot 16777216 π

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Frequently Asked Questions (FAQ)

What is 4*10^{20}(4pi) ?
The solution to 4*10^{20}(4pi) is 5^{20}*16777216pi