Question

(2x^3)^5*(2x^2)^4/(4x^5)^4=54

Answer 1

(2x^3)^5*(2x^2)^4/(4x^5)^4=54
x^(3*5)*x^(2*4)*2^5*2^4/(x^(5*4)*2^(2*4)=54
x^(15+8-20)*2^(5+4-8)=54
x^3*2=54
x^3=27
x=27^(1/3)=3

Answer 2

$\frac{(2x^3)^5*(2x^2)^4}{(4x^5)^4} = 54$

$\frac{2^5*x^{15}*2^4*x^8}{4^4x^{20}} = 54 \\ \\ \frac{(2^5*2^4)*(x^{15}*x^8)}{2^8x^{20}} = 54 \\ \\ \frac{2^9*x^{23}}{2^8x^{20}} = 54 \\ \\ 2x^{3} = 54 \\ \\ x^{3} = 27 \\ \\ x=3$

Ответ:  $x=3$

Answer 3

To simplify the given expression:

(2x^3)^5 * (2x^2)^4 / (4x^5)^4

We can start by simplifying each term individually:

(2x^3)^5 = 2^5 * (x^3)^5 = 32x^15

(2x^2)^4 = 2^4 * (x^2)^4 = 16x^8

(4x^5)^4 = 4^4 * (x^5)^4 = 256x^20

Now we can substitute these simplified terms back into the original expression:

(32x^15) * (16x^8) / (256x^20)

To divide, we subtract the exponents of x in the denominator from the exponents in the numerator:

32x^(15-8) / (256x^20)

Simplifying the exponents:

32x^7 / (256x^20)

We can simplify further by dividing both the numerator and denominator by 8:

4x^7 / (32x^20)

Dividing the coefficients:

x^7 / (8x^20)

Now, we can simplify the expression further by subtracting the exponents of x:

x^(7-20) / 8

Simplifying the exponent:

x^(-13) / 8

To express the answer without negative exponents, we can rewrite it as:

1 / (8x^13)

Therefore, the simplified expression is 1 / (8x^13), and it is not equal to 54.