Simplify the following expressions: 610/64, x12/x3, 24m2n5/4m3n2, (5⁻³)4/y2

Question

ScanSolve AI Tutor · Accepted Answer

Eyi ni bi a ṣe le yanju awọn iṣoro wọnyi:

1)

Lo ofin awọn agbara (exponents) ti o sọ pe nigba ti o ba pin awọn nọmba pẹlu ipilẹ kanna, o yọ awọn agbara wọn kuro.
$\frac{6^{10}}{6^4} = 6^{10-4}$
Yọ awọn agbara kuro.
$6^{10-4} = 6^6$
Ṣe iṣiro iye naa.
$6^6 = 6 \times 6 \times 6 \times 6 \times 6 \times 6 = 46656$
Idahun: $\boxed{46656}$

2)
Lo ofin awọn agbara ti o sọ pe nigba ti o ba pin awọn oniyipada pẹlu ipilẹ kanna, o yọ awọn agbara wọn kuro.
$\frac{x^{12}}{x^3} = x^{12-3}$
Yọ awọn agbara kuro.
$x^{12-3} = x^9$
Idahun: $\boxed{x^9}$

3)
Pin awọn nọmba ati awọn oniyipada lọtọ.
$\frac{24m^2n^5}{4m^3n^2} = \left(\frac{24}{4}\right) \left(\frac{m^2}{m^3}\right) \left(\frac{n^5}{n^2}\right)$
Ṣe iṣiro apakan nọmba ati lo ofin awọn agbara fun awọn oniyipada.
$6 \cdot m^{2-3} \cdot n^{5-2}$
Yọ awọn agbara kuro.
$6 \cdot m^{-1} \cdot n^3$
Tun kọ $m^{-1}$ bi $\frac{1}{m}$ .
$\frac{6n^3}{m}$
Idahun: $\boxed{\frac{6n^3}{m}}$

4)
Kọkọ yanju ohun ti o wa ninu akọmọ.
$(5-3)^4 = (2)^4$
Gbe abajade si agbara ti 4.
$2^4 = 2 \times 2 \times 2 \times 2 = 16$
Idahun: $\boxed{16}$

5)
Abala $y^{22}$ jẹ gbolohun ọrọ kan ti o duro nikan. Ko si iṣẹ-ṣiṣe ti o han lati yanju pẹlu rẹ.
Idahun: $\boxed{y^{22}}$

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