Simplify: 64 28m4n6/7m3n2 (4×5)3 43 × 42 (5⁻²)3

Question

ScanSolve AI Tutor · Accepted Answer

O dara, jẹ ki a rọrun awọn ikosile wọnyi ni lilo awọn ofin exponents.

1. Rọrun $\frac{6^3}{6^4}$

Lo ofin ipin fun exponents, eyiti o sọ pe $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{6^3}{6^4} = 6^{3-4}$
Ṣe iṣiro exponent naa.
$6^{3-4} = 6^{-1}$
Ranti pe $a^{-n} = \frac{1}{a^n}$ .
$6^{-1} = \boxed{\frac{1}{6}}$
2. Rọrun $\frac{28m^4n^6}{7m^3n^2}$
Pin awọn nọmba (coefficients) ati lo ofin ipin fun awọn oniyipada kọọkan.
$\frac{28m^4n^6}{7m^3n^2} = \left(\frac{28}{7}\right) \times \left(\frac{m^4}{m^3}\right) \times \left(\frac{n^6}{n^2}\right)$
Ṣe iṣiro ipin kọọkan.
$4 \times m^{4-3} \times n^{6-2}$
Ṣe iṣiro awọn exponents.
$4 \times m^1 \times n^4 = \boxed{4mn^4}$
3. Rọrun $(4x^5)^3$
Lo ofin agbara ọja, eyiti o sọ pe $(ab)^m = a^m b^m$ .
$(4x^5)^3 = 4^3 \times (x^5)^3$
Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .
$4^3 \times x^{5 \times 3}$
Ṣe iṣiro awọn agbara.
$64 \times x^{15} = \boxed{64x^{15}}$
4. Rọrun $4^3 \times 4^2$
Lo ofin isodipupo fun exponents, eyiti o sọ pe $a^m \times a^n = a^{m+n}$ .
$4^3 \times 4^2 = 4^{3+2}$
Ṣe iṣiro exponent naa.
$4^{3+2} = 4^5$
Ṣe iṣiro agbara naa.
$4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$ $\boxed{1024}$
5. Rọrun $(5^{-2})^3$
Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .
$(5^{-2})^3 = 5^{-2 \times 3}$
Ṣe iṣiro exponent naa.
$5^{-6}$
Ranti pe $a^{-n} = \frac{1}{a^n}$ .
$5^{-6} = \boxed{\frac{1}{5^6}}$

Simplify: 64 28m4n6/7m3n2 (4x5)3 43 x 42 (5⁻²)3

Step-by-step solution

Lo ofin ipin fun exponents, eyiti o sọ pe $\frac{a^m}{a^n} = a^{m-n}$ .

Ṣe iṣiro exponent naa.

Ranti pe $a^{-n} = \frac{1}{a^n}$ .

Pin awọn nọmba (coefficients) ati lo ofin ipin fun awọn oniyipada kọọkan.

Ṣe iṣiro ipin kọọkan.

Ṣe iṣiro awọn exponents.

Lo ofin agbara ọja, eyiti o sọ pe $(ab)^m = a^m b^m$ .

Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .

Ṣe iṣiro awọn agbara.

Lo ofin isodipupo fun exponents, eyiti o sọ pe $a^m \times a^n = a^{m+n}$ .

Ṣe iṣiro exponent naa.

Ṣe iṣiro agbara naa.

Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .

Ṣe iṣiro exponent naa.

Ranti pe $a^{-n} = \frac{1}{a^n}$ .

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Simplify: 64 28m4n6/7m3n2 (4x5)3 43 x 42 (5⁻²)3

Step-by-step solution

Lo ofin ipin fun exponents, eyiti o sọ pe aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n.

Ṣe iṣiro exponent naa.

Ranti pe a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1​.

Pin awọn nọmba (coefficients) ati lo ofin ipin fun awọn oniyipada kọọkan.

Ṣe iṣiro ipin kọọkan.

Ṣe iṣiro awọn exponents.

Lo ofin agbara ọja, eyiti o sọ pe (ab)m=ambm(ab)^m = a^m b^m(ab)m=ambm.

Lo ofin agbara agbara, eyiti o sọ pe (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n.

Ṣe iṣiro awọn agbara.

Lo ofin isodipupo fun exponents, eyiti o sọ pe am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Ṣe iṣiro exponent naa.

Ṣe iṣiro agbara naa.

Lo ofin agbara agbara, eyiti o sọ pe (am)n=am×n(a^m)^n = a^{m \times n}(am)n=am×n.

Ṣe iṣiro exponent naa.

Ranti pe a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1​.

Still stuck on this one?

More Mathematics Questions

Lo ofin ipin fun exponents, eyiti o sọ pe $\frac{a^m}{a^n} = a^{m-n}$ .

Ranti pe $a^{-n} = \frac{1}{a^n}$ .

Lo ofin agbara ọja, eyiti o sọ pe $(ab)^m = a^m b^m$ .

Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .

Lo ofin isodipupo fun exponents, eyiti o sọ pe $a^m \times a^n = a^{m+n}$ .

Lo ofin agbara agbara, eyiti o sọ pe $(a^m)^n = a^{m \times n}$ .

Ranti pe $a^{-n} = \frac{1}{a^n}$ .