What is 70^2*10^{-7}ln((9.7)/2)*10^4 ?

The solution to 70^2*10^{-7}ln((9.7)/2)*10^4 is 7.73699…

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simplify 70^210^{-7}ln((9.7)/2)10^4

Solution

simplify

7 0^{2} \cdot 1 0^{- 7} ln (\frac{9.7}{2}) \cdot 1 0^{4}

Solution

7.73699 \dots

Solution steps

7 0^{2} \cdot 1 0^{- 7} ln (\frac{9.7}{2}) \cdot 1 0^{4}

Apply exponent rule:

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

1 0^{- 7} \cdot 1 0^{4} = 1 0^{- 7 + 4}

= 7 0^{2} ln (\frac{9.7}{2}) \cdot 1 0^{- 7 + 4}

Add/Subtract the numbers:

- 7 + 4 = - 3

= 7 0^{2} ln (\frac{9.7}{2}) \cdot 1 0^{- 3}

Factor integer

70 = 2 \cdot 5 \cdot 7

= (2 \cdot 5 \cdot 7)^{2} ln (\frac{9.7}{2}) \cdot 1 0^{- 3}

Apply exponent rule:

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

(2 \cdot 5 \cdot 7)^{2} = 2^{2} \cdot 5^{2} \cdot 7^{2}

= 2^{2} \cdot 5^{2} \cdot 7^{2} ln (\frac{9.7}{2}) \cdot 1 0^{- 3}

Factor integer

10 = 2 \cdot 5

= 2^{2} \cdot 5^{2} \cdot 7^{2} ln (\frac{9.7}{2}) (2 \cdot 5)^{- 3}

Apply exponent rule:

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

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

= 2^{2} \cdot 5^{2} \cdot 7^{2} ln (\frac{9.7}{2}) \cdot 2^{- 3} \cdot 5^{- 3}

Apply exponent rule:

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

2^{2} \cdot 2^{- 3} = 2^{2 - 3}

= 5^{2} \cdot 7^{2} ln (\frac{9.7}{2}) \cdot 2^{2 - 3} \cdot 5^{- 3}

Subtract the numbers:

2 - 3 = - 1

= 5^{2} \cdot 7^{2} ln (\frac{9.7}{2}) \cdot 2^{- 1} \cdot 5^{- 3}

Apply exponent rule:

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

5^{2} \cdot 5^{- 3} = 5^{2 - 3}

= 7^{2} ln (\frac{9.7}{2}) \cdot 2^{- 1} \cdot 5^{2 - 3}

Subtract the numbers:

2 - 3 = - 1

= 7^{2} ln (\frac{9.7}{2}) \cdot 2^{- 1} \cdot 5^{- 1}

Apply exponent rule:

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

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

= 5^{- 1} \cdot 7^{2} \cdot \frac{1}{2} ln (\frac{9.7}{2})

Apply exponent rule:

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

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

= 7^{2} \cdot \frac{1}{2} \cdot \frac{1}{5} ln (\frac{9.7}{2})

Multiply fractions:

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

= \frac{7 ^{2} \cdot 1 \cdot 1}{2 \cdot 5} ln (\frac{9.7}{2})

\frac{1 \cdot 1 \cdot 7 ^{2}}{2 \cdot 5} = \frac{49}{10}

= \frac{49}{10} ln (\frac{9.7}{2})

Divide the numbers:

\frac{9.7}{2} = 4.85

= \frac{49}{10} ln (4.85)

Simplify

ln (4.85) : 1.57897 \dots

= 1.57897 \dots \cdot \frac{49}{10}

Simplify

= 7.73699 \dots

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Frequently Asked Questions (FAQ)

What is 70^2*10^{-7}ln((9.7)/2)*10^4 ?
The solution to 70^2*10^{-7}ln((9.7)/2)*10^4 is 7.73699…

simplify 70^2*10^{-7}ln((9.7)/2)*10^4

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 70^2*10^{-7}ln((9.7)/2)*10^4 ?

simplify 70^210^{-7}ln((9.7)/2)10^4

What is 70^210^{-7}ln((9.7)/2)10^4 ?