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Popular >

simplify 4pi(410^{-2})

Solution

simplify

4 π \cdot (4 \cdot 1 0^{- 2})

Solution

\frac{4 π}{25}

+1

Decimal Notation

0.50265 \dots

Solution steps

4 π (4 \cdot 1 0^{- 2})

Apply exponent rule:

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

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

= π 4^{1 + 1} \cdot 1 0^{- 2}

Add the numbers:

1 + 1 = 2

= π 4^{2} \cdot 1 0^{- 2}

Factor integer

4 = 2^{2}

= π (2^{2})^{2} \cdot 1 0^{- 2}

Apply exponent rule:

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

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

= π 2^{2 \cdot 2} \cdot 1 0^{- 2}

Refine

= π 2^{4} \cdot 1 0^{- 2}

Factor integer

10 = 2 \cdot 5

= π 2^{4} (2 \cdot 5)^{- 2}

Apply exponent rule:

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

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

= π 2^{4} \cdot 2^{- 2} \cdot 5^{- 2}

Apply exponent rule:

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

2^{4} \cdot 2^{- 2} = 2^{4 - 2}

= π 2^{4 - 2} \cdot 5^{- 2}

Subtract the numbers:

4 - 2 = 2

= π 2^{2} \cdot 5^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

5^{- 2} = \frac{1}{5 ^{2}}

= 2^{2} π \frac{1}{5 ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π 2 ^{2}}{5 ^{2}}

Multiply:

1 π = π

= \frac{2 ^{2} π}{5 ^{2}}

2^{2} = 4

= \frac{4 π}{5 ^{2}}

5^{2} = 25

= \frac{4 π}{25}

Popular Examples

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9.47 \cdot 1 0^{- 5}

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2.4 \cdot 1 0^{- 5} c^{- 1} \cdot 40

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13 \cdot 5 + x^{2}

simplify (3.8x10^{-6})(2.37x10^{-3})simplify

(3.8 x 1 0^{- 6}) (2.37 x 1 0^{- 3})

Frequently Asked Questions (FAQ)

What is 4pi*(4*10^{-2}) ?
The solution to 4pi*(4*10^{-2}) is (4pi)/(25)