What is -1/3 (-5)^2-2(-5)-2 ?

The solution to -1/3 (-5)^2-2(-5)-2 is -1/3

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Popular >

-1/3 (-5)^2-2(-5)-2

Solution

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

Solution

- \frac{1}{3}

Solution steps

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

Follow the PEMDAS order of operations

Calculate exponents

(- 5)^{2} : 25

(- 5)^{2}

Apply exponent rule:

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

n

is even

(- 5)^{2} = 5^{2} = 25

= 25

= - \frac{1}{3} \cdot 25 - 2 (- 5) - 2

Multiply and divide (left to right)

- \frac{1}{3} \cdot 25 : - \frac{25}{3}

- \frac{1}{3} \cdot 25

Convert element to fraction:

25 = \frac{25}{1}

= - \frac{1}{3} \cdot \frac{25}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{1}{3} \cdot \frac{25}{1} = \frac{1 \cdot 25}{3 \cdot 1}

= - \frac{1 \cdot 25}{3 \cdot 1}

Multiply the numbers:

1 \cdot 25 = 25

= - \frac{25}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{25}{3}

= - \frac{25}{3} - 2 (- 5) - 2

Multiply and divide (left to right)

2 (- 5) : - 10

2 (- 5)

Apply rule

a \cdot (- b) = - a \cdot b

2 (- 5) = - 2 \cdot 5 = - 10

= - 10

= - \frac{25}{3} - (- 10) - 2

Add and subtract (left to right)

- \frac{25}{3} - (- 10) - 2 : - \frac{1}{3}

- \frac{25}{3} - (- 10) - 2

Apply rule

- (- a) = + a

- (- 10) = + 10

= - \frac{25}{3} + 10 - 2

- \frac{25}{3} + 10 = \frac{5}{3}

- \frac{25}{3} + 10

Convert element to fraction:

10 = \frac{10 \cdot 3}{3}

= \frac{10 \cdot 3}{3} - \frac{25}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{10 \cdot 3 - 25}{3}

10 \cdot 3 - 25 = 5

10 \cdot 3 - 25

Multiply the numbers:

10 \cdot 3 = 30

= 30 - 25

Subtract the numbers:

30 - 25 = 5

= 5

= \frac{5}{3}

= \frac{5}{3} - 2

\frac{5}{3} - 2 = - \frac{1}{3}

\frac{5}{3} - 2

Convert element to fraction:

2 = \frac{2 \cdot 3}{3}

= - \frac{2 \cdot 3}{3} + \frac{5}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 \cdot 3 + 5}{3}

- 2 \cdot 3 + 5 = - 1

- 2 \cdot 3 + 5

Multiply the numbers:

2 \cdot 3 = 6

= - 6 + 5

Add/Subtract the numbers:

- 6 + 5 = - 1

= - 1

= \frac{- 1}{3}

Apply the fraction rule:

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

= - \frac{1}{3}

= - \frac{1}{3}

= - \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is -1/3 (-5)^2-2(-5)-2 ?
The solution to -1/3 (-5)^2-2(-5)-2 is -1/3