Question

\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)

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Answer 1

\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)

=\(\left(\dfrac{1}{9}\right)^{25}.\left(-9\right)^{25}-\dfrac{1}{6}\)

=\(\left[\dfrac{1}{9}.\left(-9\right)\right]^{25}-\dfrac{1}{6}\)

= \(\left(-1\right)^{25}-\dfrac{1}{6}\)

= \(-1-\dfrac{1}{6}=\dfrac{-7}{6}\)

Answer 2

\(\left(\dfrac{1}{3}\right)^{50}\cdot\left(-9\right)^{25}-\dfrac{2}{3}:4\)

\(=\left[\left(\dfrac{1}{3}\right)^2\right]^{25}\cdot\left(-9\right)^{25}-\dfrac{1}{6}\)

\(=\left(\dfrac{1}{9}\right)^{25}\cdot\left(-9\right)^{25}-\dfrac{1}{6}\)

\(=\left[\dfrac{1}{9}\cdot\left(-9\right)\right]^{25}-\dfrac{1}{6}\)

\(=\left(-1\right)^{25}-\dfrac{1}{6}=-1-\dfrac{1}{6}=-\dfrac{7}{6}\)

Answer 3

\(\dfrac{1}{3^{50}}\cdot\left(-1\right)\cdot9^{25}\)-\(\dfrac{2}{3}\cdot\dfrac{1}{4}\)

=\(\dfrac{1}{3^{50}}\cdot\left(3^2\right)^{25}\cdot\left(-1\right)-\dfrac{1}{6}\)

=\(\dfrac{1}{3^{50}}\cdot3^{50}\cdot\left(-1\right)-\dfrac{1}{6}\)

=\(1\cdot\left(-1\right)-\dfrac{1}{6}\)

=(-1)-

Answer 4

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