Thinking Mathematically (6th Edition)

A number p when gets to the power of q, it is calculated by multiplying p with p, q times. Simplifying the expression $-{{5}^{2}}$, you get: \begin{align} & -{{5}^{2}}=\left( -1 \right)\times {{5}^{2}} \\ & =-1\times 5\times 5 \end{align} $=-25$ Simplifying the expression ${{\left( -5 \right)}^{2}}$, you get: \begin{align} & {{\left( -5 \right)}^{2}}={{\left( -1 \right)}^{2}}\times {{5}^{2}} \\ & =\left( -1\times -1 \right)\times \left( 5\times 5 \right) \end{align} $=25$ Two expressions have different values and hence, they are different because of the use of brackets. It should be taken in consideration that p when gets to the power of q, is calculated by multiplying p with p, q times.