What is 1/2 (2)^4-3/4 (2)^2 ?

The solution to 1/2 (2)^4-3/4 (2)^2 is 5

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1/2 (2)^4-3/4 (2)^2

\frac{1}{2} (2)^{4} - \frac{3}{4} (2)^{2}

5

Solution steps

\frac{1}{2} (2)^{4} - \frac{3}{4} (2)^{2}

Follow the PEMDAS order of operations

Calculate exponents

(2)^{4} : 16

(2)^{4}

(2)^{4} = 16

= 16

= \frac{1}{2} \cdot 16 - \frac{3}{4} (2)^{2}

Calculate exponents

(2)^{2} : 4

(2)^{2}

(2)^{2} = 4

= 4

= \frac{1}{2} \cdot 16 - \frac{3}{4} \cdot 4

Multiply and divide (left to right)

\frac{1}{2} \cdot 16 : 8

\frac{1}{2} \cdot 16

Convert element to fraction:

16 = \frac{16}{1}

= \frac{1}{2} \cdot \frac{16}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 16}{2 \cdot 1}

\frac{1 \cdot 16}{2 \cdot 1} = 8

\frac{1 \cdot 16}{2 \cdot 1}

\frac{1 \cdot 16}{2 \cdot 1} = \frac{16}{2}

\frac{1 \cdot 16}{2 \cdot 1}

Multiply the numbers:

1 \cdot 16 = 16

= \frac{16}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{16}{2}

= \frac{16}{2}

Divide the numbers:

\frac{16}{2} = 8

= 8

= 8

= 8 - \frac{3}{4} \cdot 4

Multiply and divide (left to right)

\frac{3}{4} \cdot 4 : 3

\frac{3}{4} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{3}{4} \cdot \frac{4}{1}

Cross-cancel common factor:

4

= \frac{3}{1}

Divide the numbers:

\frac{3}{1} = 3

= 3

= 8 - 3

Add and subtract (left to right)

8 - 3 : 5

8 - 3

8 - 3 = 5

= 5

= 5

2 - \frac{1}{2} \times 3

1 5^{2} + 1 3^{2}

(- 1)^{2} - 6 (- 1) + 9

(- 2)^{2} - 4 (- 2)

- 3^{2} - 2 (- 3) + 8