What is ((1/5)^{2k})^6*(125a^2)^2 ?

The solution to ((1/5)^{2k})^6*(125a^2)^2 is 15625^{1-2k}a^4

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simplify ((1/5)^{2k})^6*(125a^2)^2

simplify

((\frac{1}{5})^{2 k})^{6} \cdot (125 a^{2})^{2}

1562 5^{1 - 2 k} a^{4}

Solution steps

((\frac{1}{5})^{2 k})^{6} (125 a^{2})^{2}

Simplify

((\frac{1}{5})^{2 k})^{6} : \frac{1}{24414062 5 ^{k}}

= \frac{1}{24414062 5 ^{k}} (125 a^{2})^{2}

Simplify

(125 a^{2})^{2} : 15625 a^{4}

= \frac{1}{24414062 5 ^{k}} \cdot 15625 a^{4}

Apply the fraction rule:

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

= \frac{1 \cdot 15625 a ^{4}}{24414062 5 ^{k}}

Multiply the numbers:

1 \cdot 15625 = 15625

= \frac{15625 a ^{4}}{24414062 5 ^{k}}

Factor

24414062 5^{k} : 1562 5^{2 k}

= \frac{15625 a ^{4}}{1562 5 ^{2 k}}

Apply exponent rule:

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

\frac{1562 5 ^{1}}{1562 5 ^{2 k}} = 1562 5^{1 - 2 k}

= 1562 5^{1 - 2 k} a^{4}

(4.425 \cdot 1 0^{- 1}) \cdot 0.05

e^{- 13.6}

\frac{x ^{c}}{y ^{c}}

0.72 e^{(- 0.0115 \cdot 8.5)}

1.602 1^{- 19} \cdot 1 0^{18}

What is ((1/5)^{2k})^6*(125a^2)^2 ?
The solution to ((1/5)^{2k})^6*(125a^2)^2 is 15625^{1-2k}a^4