What is ((-5)^2*25^3)/(5^{10)} ?

The solution to ((-5)^2*25^3)/(5^{10)} is 1/25

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simplify ((-5)^2*25^3)/(5^{10)}

simplify

\frac{( - 5 ) ^{2} \cdot 2 5 ^{3}}{5 ^{10}}

\frac{1}{25}

Solution steps

\frac{( - 5 ) ^{2} \cdot 2 5 ^{3}}{5 ^{10}}

Factor

2 5^{3} : 5^{6}

= \frac{( - 5 ) ^{2} \cdot 5 ^{6}}{5 ^{10}}

\frac{5 ^{6}}{5 ^{10}} = \frac{1}{5 ^{4}}

= \frac{( - 5 ) ^{2}}{5 ^{4}}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= \frac{5 ^{2}}{5 ^{4}}

Apply exponent rule:

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

= \frac{1}{5 ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

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

5^{2} = 25

= \frac{1}{25}

2 \cdot 2^{2}

6 x (x - 3) < 2 (3 x - 1) (x - 4)

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x^{2} + 8 x - 65 = x - 5