Answer:
[tex]\frac{145}{24}[/tex]
Step-by-step explanation:
[tex]((2*3)^{-1} -(2^{3}) ^{-1} )+(\frac{1}{2} -\frac{1}{3} )^{-1} \\[/tex]
[tex](2^{-1} *3^{-1} -2^{-3} )+(\frac{3+2(-1)}{2*3} )^{-1}[/tex]
[tex]\frac{145}{24}[/tex]
Answer:
6 1/24
Step-by-step explanation:
x⁻² = 1 / x² - in other words, when a number has an exponent of -1, you simply invert the number. 6⁻¹ is simply 1/6.
rewriting your equation you would have:
(1/6 - 1/8) + ( 1/2 - 1/3)⁻¹ leave the last exponent alone for now
Find a common denominator for all 4 fractions.
common denominator is 24 since it's divisible by 2, 3, 6 and 8
rewrite the equation again
(4/24 - 3/24) + (12/24 - 8/24)⁻¹
do the math inside the parentheses
( 1/24) + (4/24)⁻¹ since this last fraction has an exponent of -1, then that fraction gets inverted or flipped upside down.
1/24 + 24/4
24/4 is the same as 6 so your answer would be 6 1/24