Question

2^(-3)+6^(-1)-2*4^(-3)

Answer 1

$2^{-3}+6^{-1} =\frac{1}{2^{3} }+\frac{1}{6}=\frac{1}{8}+\frac{1}{6} =\frac{3+4}{24}=\frac{7}{24}\\\\-2*4^{-3} =-2*\frac{1}{4^{3}}=-2*\frac{1}{64}=-\frac{1}{32}=-0,03125$

Answer 2

To simplify the expression 2^(-3) + 6^(-1) - 2 * 4^(-3), you can first calculate the values of each term and then perform the arithmetic operations.

1. 2^(-3) means "2 raised to the power of -3," which is equivalent to 1 divided by 2^3, or 1/8.
2. 6^(-1) means "6 raised to the power of -1," which is equivalent to 1 divided by 6, or 1/6.
3. 4^(-3) means "4 raised to the power of -3," which is equivalent to 1 divided by 4^3, or 1/64.

Now, let's plug these values back into the expression:

1/8 + 1/6 - 2 * 1/64

To add these fractions, you need a common denominator, which in this case is 64. So, let's find equivalent fractions with a denominator of 64:

(1/8) = (8/64) (1/6) = (10/64)

Now, rewrite the expression with a common denominator:

(8/64) + (10/64) - 2 * (1/64)

Now, you can add and subtract these fractions:

(8/64) + (10/64) - (2/64)

Now, add the fractions:

(8 + 10 - 2) / 64

Combine the numerators:

16 / 64

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 16:

(16 ÷ 16) / (64 ÷ 16) = 1/4

So, the simplified value of the expression 2^(-3) + 6^(-1) - 2 * 4^(-3) is 1/4.