Question

1. tersley solved three different problems on her math test. circle the problem she solved incorrectly. explain her error and find the correct answer.

simplify ( 8 ^ { 3 } )
( 8 cdot 8 cdot 8 )
512
simplify ( 13 cdot 5 ^ { 2 } )
( 3 cdot 25 )
75
simplify ( 5 ^ { 2 } cdot 7 )
( 125 cdot 7 )
875

Explanation:

Step1: Calculate \(8^{3}\)

\(8^{3}=8\times8\times8 = 512\)

Step2: Calculate \(13.5^{2}\)

\(13.5^{2}=13.5\times13.5=(13 + 0.5)\times(13+0.5)=13^{2}+2\times13\times0.5 + 0.5^{2}=169+13 + 0.25=182.25
eq3.25\)

Step3: Calculate \(5^{3}\times7\)

\(5^{3}\times7=(5\times5\times5)\times7=125\times7 = 875\)

Answer:

The first problem \(8^{3}\) is calculated correctly with the answer \(512\). The second problem \(13.5^{2}\) is calculated incorrectly (correct answer \(182.25\)). The third problem \(5^{3}\times7\) is calculated correctly with the answer \(875\).