What is 4-4\div 4^2-16 ?

The solution to 4-4\div 4^2-16 is -49/4

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4-4\div 4^2-16

4 - 4 \div 4^{2} - 16

- \frac{49}{4}

Solution steps

4 - 4 \div 4^{2} - 16

Follow the PEMDAS order of operations

Calculate exponents

4^{2} : 16

4^{2}

4^{2} = 16

= 16

= 4 - 4 \div 16 - 16

Multiply and divide (left to right)

4 \div 16 : \frac{4}{16}

4 \div 16

4 \div 16 = \frac{4}{16}

= \frac{4}{16}

= 4 - \frac{4}{16} - 16

Add and subtract (left to right)

4 - \frac{4}{16} - 16 : - \frac{49}{4}

4 - \frac{4}{16} - 16

4 - \frac{4}{16} = \frac{15}{4}

4 - \frac{4}{16}

Cancel

\frac{4}{16} : \frac{1}{4}

\frac{4}{16}

Cancel the common factor:

4

= \frac{1}{4}

= 4 - \frac{1}{4}

Convert element to fraction:

4 = \frac{4 \cdot 4}{4}

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

Since the denominators are equal, combine the fractions:

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

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

4 \cdot 4 - 1 = 15

4 \cdot 4 - 1

Multiply the numbers:

4 \cdot 4 = 16

= 16 - 1

Subtract the numbers:

16 - 1 = 15

= 15

= \frac{15}{4}

= \frac{15}{4} - 16

\frac{15}{4} - 16 = - \frac{49}{4}

\frac{15}{4} - 16

Convert element to fraction:

16 = \frac{16 \cdot 4}{4}

= - \frac{16 \cdot 4}{4} + \frac{15}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{- 16 \cdot 4 + 15}{4}

- 16 \cdot 4 + 15 = - 49

- 16 \cdot 4 + 15

Multiply the numbers:

16 \cdot 4 = 64

= - 64 + 15

Add/Subtract the numbers:

- 64 + 15 = - 49

= - 49

= \frac{- 49}{4}

Apply the fraction rule:

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

= - \frac{49}{4}

= - \frac{49}{4}

= - \frac{49}{4}

3 \times (- 3)^{2} - 4 \times (- 3) + 2

4 8^{2} + 6 4^{2}

- 3 - 4 \times 5 \times 4 \div 2 - 5

10 \div 5 (1 - 3)

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