Evaluate:7^0 (25)^ -3 2 -5^ -3 - Vidyadip

Question

Evaluate$:7^0 \times(25)^{-\frac{3}{2}}-5^{-3}$

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Answer

$ 7^0 \times(25)^{-\frac{3}{2}}-5^{-3}$
$ =7^0 \times(5 \times 5)^{-\frac{3}{2}}-5^{-3}$
$ =7^0 \times\left(5^2\right)^{-\frac{3}{2}}-\frac{1}{5^3}$
$ =7^0 \times\left[(5)^{2 \times\left(-\frac{3}{2}\right)}\right]-\frac{1}{5^3}$
$ =7^0 \times 5^{-3}-\frac{1}{5^3}$
$ =1 \times 5^{-3}-\frac{1}{5^3}$
$ =\frac{1}{5^3}-\frac{1}{5^3}$
$ =\frac{1-1}{5 \times 5 \times 5}$
$ =\frac{0}{125}$
$ =0$

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