What is 1/2 5(2-10)^2 ?

The solution to 1/2 5(2-10)^2 is 160

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1/2 5(2-10)^2

\frac{1}{2} 5 (2 - 10)^{2}

160

Solution steps

\frac{1}{2} \cdot 5 (2 - 10)^{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(2 - 10) : - 8

2 - 10

2 - 10 = - 8

= - 8

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

Calculate exponents

(- 8)^{2} : 64

(- 8)^{2}

Apply exponent rule:

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

n

is even

(- 8)^{2} = 8^{2} = 64

= 64

= \frac{1}{2} \cdot 5 \cdot 64

Multiply and divide (left to right)

\frac{1}{2} \cdot 5 \cdot 64 : 160

\frac{1}{2} \cdot 5 \cdot 64

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

\frac{1}{2} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{1}{2} \cdot \frac{5}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 5}{2 \cdot 1}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{5}{2}

= \frac{5}{2} \cdot 64

\frac{5}{2} 64 = 160

\frac{5}{2} \cdot 64

Convert element to fraction:

64 = \frac{64}{1}

= \frac{5}{2} \cdot \frac{64}{1}

Apply the fraction rule:

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

= \frac{5 \cdot 64}{2 \cdot 1}

Cancel

\frac{5 \cdot 64}{2 \cdot 1} : 160

\frac{5 \cdot 64}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{5 \cdot 64}{2}

Divide the numbers:

\frac{64}{2} = 32

= 5 \cdot 32

Multiply the numbers:

5 \cdot 32 = 160

= 160

= 160

= 160

= 160

- 4 \times 1 \times (- 5)

1 \div 9 \times 1 \div 2

2 \times (12 \div 2)^{2} - 14 + 6

(- 2)^{3} - 8

(10 \div 5) \times 5 - 4