Question

Solve que4

Q4. Simplify and express the result with positive exponent or a rational number. (– 5)² × (125)² × (5)^–3.

Answer 1

Dear Student,

$$\begin{gathered} {\left(-5\right)}^2\times {\left(125\right)}^2\times {\left(5\right)}^{-3} \\ \Rightarrow {\left(-5\right)}^2\times {\left[{\left(5\right)}^3\right]}^2\times {\left(5\right)}^{-3} \\ \Rightarrow {\left(-5\right)}^2\times {\left(5\right)}^6\times {\left(5\right)}^{-3} \\ \Rightarrow {\left(-5\right)}^2\times 5^{6-3}\left[\mathit{U}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathbf{}{\mathit{a}}^{\mathbf{b}}\mathbf{\times }{\mathit{a}}^{\mathbf{c}}\mathbf{=}{\mathit{a}}^{\mathbf{b}\mathbf{+}\mathbf{c}}\right] \\ \Rightarrow {\left(-5\right)}^2\times 5^3 \\ \Rightarrow {\left(-1\right)}^2\times {\left(5\right)}^2\times {\left(5\right)}^3 \\ \Rightarrow 5^{2+3} \\ \Rightarrow {\mathbf{5}}^{\mathbf{5}} \end{gathered}$$

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