Question 3 - Figure it out - Page 44, 45 - Chapter 2 Class 8 - Power Play (Ganita Prakash)

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Question 3 Write the given number as the product of two or more powers in three different ways. The powers can be any integers. (i) 643Second way Since 𝟖^𝟐=𝟔𝟒, Now, 〖𝟔𝟒〗^𝟑=(8^2 )^3=8^(2 × 3)=𝟖^𝟔 And, we can write 𝟖^𝟔=8^(2+4)=𝟖^𝟐 × 𝟖^𝟒 Thus, 〖𝟔𝟒〗^𝟑= 𝟖^𝟐 × 𝟖^𝟒 Third way 〖𝟔𝟒〗^𝟑=64^(5−2) =〖𝟔𝟒〗^𝟓/〖𝟔𝟒〗^𝟐 =〖𝟔𝟒〗^𝟓 × 〖𝟔𝟒〗^(−𝟐) Question 3 Write the given number as the product of two or more powers in three different ways. The powers can be any integers. (ii) 1928First way 〖𝟏𝟗𝟐〗^𝟖=192^(6+2) =〖𝟏𝟗𝟐〗^𝟔 × 〖𝟏𝟗𝟐〗^𝟐 Second way Since 𝟏𝟗𝟐=𝟑 × 𝟔𝟒, Now, 〖𝟏𝟗𝟐〗^𝟖=(3 × 64)^8 =𝟑^𝟖 × 〖𝟔𝟒〗^𝟖 Third way 〖𝟏𝟗𝟐〗^𝟖=192^(10−2) =〖𝟏𝟗𝟐〗^𝟏𝟎/〖𝟏𝟗𝟐〗^𝟐 =〖𝟏𝟗𝟐〗^𝟏𝟎 × 〖𝟏𝟗𝟐〗^(−𝟐) Question 3 Write the given number as the product of two or more powers in three different ways. The powers can be any integers. (iii) 32–5First way 〖𝟑𝟐〗^(−𝟓)=32^(−(2+3)) =32^(−2−3) =〖𝟑𝟐〗^(−𝟐) × 〖𝟑𝟐〗^(−𝟑) Second way Since 𝟑𝟐=𝟐 × 𝟏𝟔, Now, 〖𝟑𝟐〗^(−𝟓)=(2 × 16)^(−5) =𝟐^(−𝟓) × 〖𝟏𝟔〗^(−𝟓) Third way 〖𝟑𝟐〗^(−𝟓)=32^(−(8−3) ) =32^(−8 + 3 ) =〖𝟑𝟐〗^(−𝟖) × 〖𝟑𝟐〗^𝟑