7: simplify: a4 / a3 x a6 8: solve 3n+6/5 = 2+n (3 marks)

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7. Simplify: $a^4 \div a^3 \times a^6$

Tunatumia sheria za exponents (nguvu) hapa. Wakati wa kugawanya exponents zenye base (msingi) sawa, tunatoa exponents. Wakati wa kuzidisha exponents zenye base sawa, tunajumlisha exponents. Tunafuata utaratibu wa shughuli (division kwanza, kisha multiplication).

Fanya mgawanyiko kwanza.
$a^4 \div a^3 = a^{4-3} = a^1 = a$
Fanya kuzidisha.
$a \times a^6 = a^{1+6} = a^7$
Jibu la mwisho:
$\boxed{a^7}$
8. Solve $\frac{3n+6}{5} = 2+n$

Huu ni mlinganyo wa linear. Lengo ni kutafuta thamani ya $n$ .
Ondoa kigawanyo kwa kuzidisha pande zote mbili za mlinganyo kwa 5.
$5 \times \left(\frac{3n+6}{5}\right) = 5 \times (2+n)$ $3n+6 = 10+5n$
Kusanya vigezo vya $n$ upande mmoja na nambari upande mwingine.
Toa $3n$ kutoka pande zote mbili:
$6 = 10 + 5n - 3n$ $6 = 10 + 2n$
Toa 10 kutoka pande zote mbili:
$6 - 10 = 2n$ $-4 = 2n$
Gawanya kwa 2 ili kupata thamani ya $n$ .
$n = \frac{-4}{2}$ $n = -2$
Jibu la mwisho:
$\boxed{-2}$

7: simplify: a4 / a3 x a6 8: solve 3n+6/5 = 2+n (3 marks)

Answer

Step-by-step solution

Fanya mgawanyiko kwanza.

Fanya kuzidisha.

Ondoa kigawanyo kwa kuzidisha pande zote mbili za mlinganyo kwa 5.

Kusanya vigezo vya $n$ upande mmoja na nambari upande mwingine.

Gawanya kwa 2 ili kupata thamani ya $n$ .

Try one yourself

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7: simplify: a4 / a3 x a6 8: solve 3n+6/5 = 2+n (3 marks)

Answer

Step-by-step solution

Fanya mgawanyiko kwanza.

Fanya kuzidisha.

Ondoa kigawanyo kwa kuzidisha pande zote mbili za mlinganyo kwa 5.

Kusanya vigezo vya nnn upande mmoja na nambari upande mwingine.

Gawanya kwa 2 ili kupata thamani ya nnn.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Kusanya vigezo vya $n$ upande mmoja na nambari upande mwingine.

Gawanya kwa 2 ili kupata thamani ya $n$ .