A digital display records the number of operations carried out by a computer as 22×23. (a) Simplify the…

Question

A digital display records the number of operations carried out by a computer as 22×23. (a) Simplify the expression, leaving your answer in index form. (b) Hence, write the answer as an ordinary number. (c) Simplify: 54 × 54 / 53

ScanSolve AI Tutor · Accepted Answer

Huu hapa ni ufumbuzi wa swali la 22. Swali la 22: A digital display records the number of operations carried out by a computer as 2ⁿ × 2¹. a) Rahisisha usemi, ukiacha jibu lako katika fomu ya 'index'. Step 1: Tumia sheria ya 'indices' inayosema kwamba unapozidisha namba zenye 'base' sawa, unaongeza 'powers' zake: a^m × aⁿ = a^(m+n). 2ⁿ × 2¹ = 2ⁿ⁺¹ Jibu ni 2ⁿ⁺¹. b) Kwa hivyo, andika jibu kama nambari ya kawaida. Haiwezekani kuandika 2ⁿ⁺¹ kama nambari ya kawaida bila kujua thamani maalum ya 'n'. c) Rahisisha: (5⁴ × 5⁴)/(5³) Step 1: Rahisisha nambari ya juu (numerator) kwa kutumia sheria ya 'indices' a^m × aⁿ = a^(m+n). 5⁴ × 5⁴ = 5⁴⁺⁴ = 5⁸; Step 2: Rahisisha usemi mzima kwa kutumia sheria ya 'indices' inayosema kwamba unapotenganisha namba zenye 'base' sawa, unatoa 'powers' zake: (a^m)/(aⁿ) = a^(m−n). (5⁸)/(5³) = 5⁸⁻³ = 5⁵ Jibu ni 5⁵.

A digital display records the number of operations carried out by a computer as 22x23. (a) Simplify the expression, leaving your answer in index form. (b) Hence, write the answer as an ordinary number. (c) Simplify: 54 x 54 / 53

Answers

Step-by-step solution

Part 22

Part a· 1 step
$2^{n+1}$

Tumia sheria ya 'indices' inayosema kwamba unapozidisha namba zenye 'base' sawa, unaongeza 'powers' zake

Part b

Part c· 2 steps
$5^5$

Rahisisha nambari ya juu (numerator) kwa kutumia sheria ya 'indices' $a^m \times a^n = a^{m+n}$ .

Rahisisha usemi mzima kwa kutumia sheria ya 'indices' inayosema kwamba unapotenganisha namba zenye 'base' sawa, unatoa 'powers' zake

Try one yourself

Still stuck on this one?

More Mathematics Questions