Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$(9^{0}\times16^{-2})\times2^{2}; [(\frac{-8}{13})^{-1}+(\frac{14}{5})^{-1}]+(\frac{7}{5})^{-1}$$

Answer

$$1*1/256*2^2;[(-8/13)^-1+5^1]/14^1]+5/7$$

Solution


Use Rule of Zero: \({x}^{0}=1\).
1*16^-2*2^2;\({(-\frac{8}{13})}^{-1}+{(\frac{14}{5})}^{-1}\)+(7/5)^-1
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
1*1/16^2*2^2;\({(-\frac{8}{13})}^{-1}+{(\frac{14}{5})}^{-1}\)+(7/5)^-1
Simplify  \({16}^{2}\)  to  \(256\).
1*1/256*2^2;\({(-\frac{8}{13})}^{-1}+{(\frac{14}{5})}^{-1}\)+(7/5)^-1
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
1*1/256*2^2;\({(-\frac{8}{13})}^{-1}+\frac{1}{{(\frac{14}{5})}^{1}}\)+(7/5)^-1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
Invert and multiply.
Invert and multiply.
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