Question

(2^3а^-3)^-1*64а^-4, при а=-0,125

Answer 1

Ответ:

-64

Объяснение:

$\tt\displaystyle (2^{3}*x^{-3})^{-1}*64a^{-4}=2^{3*(-1)}*a^{-3*(-1)}*2^{6}a^{-4}=2^{-3}a^{3}*2^{6}a^{-4}=\\\\=2^{-3}*2^{6}*a^{3}a^{-4}=2^{-3+6}*a^{3+(-4)}=2^{3}*a^{-1}=\frac{2^{3} }{a}=\frac{8}{a}$

при a = -0,125

$\tt\displaystyle \frac{8}{a}=\frac{8}{-0,125}=-64$

Answer 2

To solve this expression, let's substitute the value of 'a' into the given expression and simplify it.

Given expression: (2^3a^-3)^-1 * 64a^-4

Substituting a = -0.125 into the expression: (2^3(-0.125)^-3)^-1 * 64(-0.125)^-4

Now, let's simplify each part of the expression step by step.

1. Simplifying the exponent of -0.125: (-0.125)^-3 = (-1/0.125)^3 = (-8)^3 = -512

2. Simplifying the exponent of -0.125 in the second part: (-0.125)^-4 = (-1/0.125)^4 = (-8)^4 = 4096

3. Simplifying the base of 2^3: 2^3 = 2 * 2 * 2 = 8

Now, substitute the simplified values back into the expression:

(8 * -512)^-1 * (64 * 4096)

Simplifying further:

(-4096)^-1 * 262,144

The reciprocal of -4096 is -1/4096, so:

(-1/4096) * 262,144 = -262,144/4096 = -64

Therefore, when a = -0.125, the expression (2^3a^-3)^-1 * 64a^-4 is equal to -64.