What is (10^3*100^2*1000^4)/((10^2)^5*100) ?

The solution to (10^3*100^2*1000^4)/((10^2)^5*100) is 10000000

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simplify (10^3100^21000^4)/((10^2)^5*100)

simplify

\frac{1 0 ^{3} \cdot 10 0 ^{2} \cdot 100 0 ^{4}}{( 1 0 ^{2} ) ^{5} \cdot 100}

10000000

Solution steps

\frac{1 0 ^{3} \cdot 10 0 ^{2} \cdot 100 0 ^{4}}{( 1 0 ^{2} ) ^{5} \cdot 100}

(1 0^{2})^{5} = 1 0^{10}

= \frac{1 0 ^{3} \cdot 10 0 ^{2} \cdot 100 0 ^{4}}{1 0 ^{10} \cdot 100}

\frac{10 0 ^{2}}{100} = 100

= \frac{1 0 ^{3} \cdot 100 \cdot 100 0 ^{4}}{1 0 ^{10}}

\frac{1 0 ^{3}}{1 0 ^{10}} = \frac{1}{1 0 ^{7}}

= \frac{100 \cdot 100 0 ^{4}}{1 0 ^{7}}

Factor the number:

100 = 1 0^{2}

= \frac{1 0 ^{2} \cdot 100 0 ^{4}}{1 0 ^{7}}

\frac{1 0 ^{2}}{1 0 ^{7}} = \frac{1}{1 0 ^{5}}

= \frac{100 0 ^{4}}{1 0 ^{5}}

Factor

100 0^{4} : 1 0^{12}

= \frac{1 0 ^{12}}{1 0 ^{5}}

Apply exponent rule:

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

= 1 0^{12 - 5}

Subtract the numbers:

12 - 5 = 7

= 1 0^{7}

1 0^{7} = 10000000

= 10000000

\frac{- 4 + 8 i}{- 6 i}

x^{8} - 81 y^{8}

(\frac{1}{2} - \frac{1}{2} i)^{- 7}

(5 a - 8)^{3}

What is (10^3*100^2*1000^4)/((10^2)^5*100) ?
The solution to (10^3*100^2*1000^4)/((10^2)^5*100) is 10000000