Question

p-84 dividing exp/neg exp

1. \frac{15 m^{12} n^5 d^8}{5 m^5 n^3 d^2} =

1. \frac{3 a^9 b^8 c^{12}}{13 a^7 b^4 c^9} =

1. (7^8)^3 =

1. 17x^2 \cdot 3x^2 \cdot 2x^3 =

\frac{12 x^{12} y^{17}}{15 x^8 y^4} =

\frac{28 a^4 b^8 z^4}{24 a^5 b^2 z^5} =

2 a^3 b^5 \cdot 7 a^5 b =

(5 x y^3)^3 =

Explanation:

Orient the image and identify the problems

The image is upside down. Rotating it 180 degrees reveals 8 algebraic simplification problems involving exponent rules:

1. \(\frac{12x^{12}y^{17}}{15x^8y^4}\)
2. \(\frac{28a^4b^4}{24a^5b^2z^5}\)
3. \(\frac{15m^{12}n^5d^8}{5m^5n^3d^2}\)
4. \(\frac{13w^7y^4}{12w^3y^9}\)
5. \(2a^2b^3 \cdot 7a^5b\)
6. \((7b^3)^3\)
7. \((5xy^3)^3\)
8. \(17x^2 \cdot 3x^2 \cdot 2x^3\)

Simplify each expression

• Problem 1:

$$ \frac{12x^{12}y^{17}}{15x^8y^4} = \frac{4}{5}x^{12-8}y^{17-4} = \frac{4x^4y^{13}}{5} $$

• Problem 2:

$$ \frac{28a^4b^4}{24a^5b^2z^5} = \frac{7}{6}a^{4-5}b^{4-2}z^{-5} = \frac{7b^2}{6az^5} $$

• Problem 3:

$$ \frac{15m^{12}n^5d^8}{5m^5n^3d^2} = 3m^{12-5}n^{5-3}d^{8-2} = 3m^7n^2d^6 $$

• Problem 4:

$$ \frac{13w^7y^4}{12w^3y^9} = \frac{13}{12}w^{7-3}y^{4-9} = \frac{13w^4}{12y^5} $$

• Problem 5:

$$ 2a^2b^3 \cdot 7a^5b = (2 \cdot 7)a^{2+5}b^{3+1} = 14a^7b^4 $$

• Problem 6:

$$ (7b^3)^3 = 7^3(b^3)^3 = 343b^9 $$

• Problem 7:

$$ (5xy^3)^3 = 5^3x^3(y^3)^3 = 125x^3y^9 $$

• Problem 8:

$$ 17x^2 \cdot 3x^2 \cdot 2x^3 = (17 \cdot 3 \cdot 2)x^{2+2+3} = 102x^7 $$

Format the final output

Since there are 8 short-answer questions, we present them in a clean standard table.

Answer:

No.	Problem	Answer
2	\(\frac{28a^4b^4}{24a^5b^2z^5}\)	\(\frac{7b^2}{6az^5}\)
3	\(\frac{15m^{12}n^5d^8}{5m^5n^3d^2}\)	\(3m^7n^2d^6\)
4	\(\frac{13w^7y^4}{12w^3y^9}\)	\(\frac{13w^4}{12y^5}\)
5	\(2a^2b^3 \cdot 7a^5b\)	\(14a^7b^4\)
6	\((7b^3)^3\)	\(343b^9\)
7	\((5xy^3)^3\)	\(125x^3y^9\)
8	\(17x^2 \cdot 3x^2 \cdot 2x^3\)	\(102x^7\)