Question

A)100000 * ((-0,1x^3 y^4)^2)^3 b) ((-1/5m^2 n)^2 * 5mp)^3

Answer 1

a)

$100000\cdot ((-0,1x^3 y^4)^2)^3=10^5\cdot ((-0,1)^2x^6 y^8)^3=10^5\cdot (-0,1)^6x^{18} y^{24}=\frac{x^{18} y^{24}}{10}$

b)

$((-\frac{1}{5}m^2 n)^2\cdot 5mp)^3= ((-\frac{1}{5})^2m^4 n^2\cdot 5mp)^3= (\frac{1}{25}m^5 n^2\cdot 5p)^3=(\frac{1}{5}m^5 n^2p)^3=\frac{m^{15}n^6p^3}{125}$

Answer 2

Let's simplify the given expressions:

A) 100000 * ((-0.1x^3 y^4)^2)^3

To simplify, we'll start from the innermost parentheses and work our way out:

(-0.1x^3 y^4)^2 = (-0.1)^2 * (x^3)^2 * (y^4)^2 = 0.01 * x^(32) * y^(42) = 0.01 * x^6 * y^8

Now, we can substitute this back into the original expression:

100000 * ((-0.1x^3 y^4)^2)^3 = 100000 * (0.01 * x^6 * y^8)^3 = 100000 * (0.0001 * x^18 * y^24) = 10 * x^18 * y^24

Therefore, the simplified expression for A) is 10 * x^18 * y^24.

B) ((-1/5m^2 n)^2 * 5mp)^3

Again, let's start from the innermost parentheses:

(-1/5m^2 n)^2 = (-1/5)^2 * (m^2)^2 * n^2 = (1/25) * m^(2*2) * n^2 = (1/25) * m^4 * n^2

Now, we can substitute this back into the original expression:

((1/25) * m^4 * n^2 * 5mp)^3 = ((1/25) * 5mp * m^4 * n^2)^3 = (1/25)^3 * (5)^3 * (m^4)^3 * (n^2)^3 * (p^3)^3 = (1/25)^3 * 125 * m^(43) * n^(23) * p^9 = (1/15625) * 125 * m^12 * n^6 * p^9 = (5/125) * m^12 * n^6 * p^9 = (1/25) * m^12 * n^6 * p^9 = m^12 * n^6 * p^9 / 25

Therefore, the simplified expression for B) is m^12 * n^6 * p^9 / 25.