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

The solution to 1/3(5)^2(5+1) is 50

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

1/3 (5)^{2} (5 + 1)

50

Solution steps

1/3 (5)^{2} (5 + 1)

Follow the PEMDAS order of operations

Calculate within parentheses

(5 + 1) : 6

5 + 1

5 + 1 = 6

= 6

= 1/3 (5)^{2} \cdot 6

Calculate exponents

(5)^{2} : 25

(5)^{2}

(5)^{2} = 25

= 25

= 1/3 \cdot 25 \cdot 6

Multiply and divide (left to right)

1/3 \cdot 25 \cdot 6 : 50

1/3 \cdot 25 \cdot 6

1/3 = \frac{1}{3}

= \frac{1}{3} \cdot 25 \cdot 6

\frac{1}{3} 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 \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} \cdot 6

\frac{25}{3} 6 = 50

\frac{25}{3} \cdot 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{25}{3} \cdot \frac{6}{1}

Apply the fraction rule:

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

= \frac{25 \cdot 6}{3 \cdot 1}

Cancel

\frac{25 \cdot 6}{3 \cdot 1} : 50

\frac{25 \cdot 6}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{25 \cdot 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 25 \cdot 2

Multiply the numbers:

25 \cdot 2 = 50

= 50

= 50

= 50

= 50

6 (2) - 3 (2)^{2}

5 - (- \frac{1}{9}) - \frac{17}{2}

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

3^{2} - 8^{2}

- (+ 1) - (+ 3) - (- 4) - (- 5)