1 a) i) Evaluate 25 1/23 ii) Simplify 3x2y3 2x3y⁻¹ iii) Solve for x, given that 3x2 - 8 = 10.75.

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Haya hapa masuluhisho ya maswali yako: a) i) Evaluate 2⁵ × (1)/(2³) Step 1: Andika (1)/(2³) kama kielelezo hasi. (1)/(2³) = 2⁻³; Step 2: Tumia sheria ya vipeo a^m × aⁿ = a^(m+n). 2⁵ × 2⁻³ = 2⁵⁺⁽⁻³⁾ = 2⁵⁻³ Step 3: Rahisisha kielelezo na hesabu. 2⁵⁻³ = 2² = 4 Jibu ni 4. ii) Simplify 3x²y³ × 2x³y⁻¹ Step 1: Panga upya maneno ili kuzidisha coefficients na vigezo tofauti. 3x²y³ × 2x³y⁻¹ = (3 × 2) × (x² × x³) × (y³ × y⁻¹) Step 2: Zidisha coefficients. 3 × 2 = 6; Step 3: Tumia sheria ya vipeo a^m × aⁿ = a^(m+n) kwa vigezo x na y. x² × x³ = x²⁺³ = x⁵; y³ × y⁻¹ = y³⁺⁽⁻¹⁾ = y³⁻¹ = y² Step 4: Unganisha matokeo. 6x⁵y² Jibu ni 6x⁵y². iii) Solve for x, given that 3x² − 8 = 10.75. Step 1: Ongeza 8 pande zote mbili za mlinganyo ili kutenga neno la x². 3x² − 8 + 8 = 10.75 + 8; 3x² = 18.75 Step 2: Gawanya pande zote mbili kwa 3 ili kupata x². (3x²)/(3) = 18.75/3; x² = 6.25 Step 3: Chukua mzizi wa mraba wa pande zote mbili ili kupata x. Kumbuka kuwa kuna suluhisho chanya na hasi. x = ±√(6.25); x = ± 2.5; Jibu ni x = ± 2.5.

1 a) i) Evaluate 25 1/23 ii) Simplify 3x2y3 2x3y⁻¹ iii) Solve for x, given that 3x2 − 8 = 10.75.

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Step-by-step solution

Part a· 3 steps

Andika $\frac{1}{2^3}$ kama kielelezo hasi.

Tumia sheria ya vipeo $a^m \times a^n = a^{m+n}$ .

Rahisisha kielelezo na hesabu.

Part a(ii)· 4 steps
$6x^5y^2$

Panga upya maneno ili kuzidisha coefficients na vigezo tofauti.

Zidisha coefficients.

Tumia sheria ya vipeo $a^m \times a^n = a^{m+n}$ kwa vigezo $x$ na $y$ .

Unganisha matokeo.

Part a(iii)· 3 steps
$x = \pm 2.5$

Ongeza 8 pande zote mbili za mlinganyo ili kutenga neno la $x^2$ .

Gawanya pande zote mbili kwa 3 ili kupata $x^2$ .

Chukua mzizi wa mraba wa pande zote mbili ili kupata $x$ .

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