What is [((-5+1))/2 ]^3-7 ?

The solution to [((-5+1))/2 ]^3-7 is -15

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simplify [((-5+1))/2 ]^3-7

simplify

[\frac{( - 5 + 1 )}{2}]^{3} - 7

- 15

Solution steps

(\frac{- 5 + 1}{2})^{3} - 7

(\frac{- 5 + 1}{2})^{3} = - 8

(\frac{- 5 + 1}{2})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 5 + 1 ) ^{3}}{2 ^{3}}

(- 5 + 1)^{3} = - 64

(- 5 + 1)^{3}

Add the numbers:

- 5 + 1 = - 4

= (- 4)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 4)^{3} = - 4^{3}

= - 4^{3}

4^{3} = 64

= - 64

= \frac{- 64}{2 ^{3}}

2^{3} = 8

= \frac{- 64}{8}

\frac{- 64}{8} = - 8

\frac{- 64}{8}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{64}{8}

Divide the numbers:

\frac{64}{8} = 8

= - 8

= - 8

= - 8 - 7

Subtract the numbers:

- 8 - 7 = - 15

= - 15

\frac{2}{2} (2 + 2)

2^{3} \cdot 3^{2}

1 0^{2} + \frac{( 5 \cdot 16 )}{10} + (43 \cdot 4)

\frac{125}{8}

\frac{12}{13}