Solve 7w^53w-15 - ScanMath

Question

Simplify the expression

21 w^{6} - 15

Evaluate

7 w^{5} \times 3 w - 15

Solution

More Steps

Evaluate

7 w^{5} \times 3 w

Multiply the terms

21 w^{5} \times w

Multiply the terms with the same base by adding their exponents

21 w^{5 + 1}

Add the numbers

21 w^{6}

21 w^{6} - 15

Show Solution

Factor the expression

3 (7 w^{6} - 5)

Evaluate

7 w^{5} \times 3 w - 15

Multiply

More Steps

Evaluate

7 w^{5} \times 3 w

Multiply the terms

21 w^{5} \times w

Multiply the terms with the same base by adding their exponents

21 w^{5 + 1}

Add the numbers

21 w^{6}

21 w^{6} - 15

Solution

3 (7 w^{6} - 5)

Show Solution

Find the roots

w_{1} = - \frac{6 84035}{7}, w_{2} = \frac{6 84035}{7}

Alternative Form

w_{1} \approx - 0.945465, w_{2} \approx 0.945465

Evaluate

7 w^{5} \times 3 w - 15

To find the roots of the expression,set the expression equal to 0

7 w^{5} \times 3 w - 15 = 0

Multiply

More Steps

Multiply the terms

7 w^{5} \times 3 w

Multiply the terms

21 w^{5} \times w

Multiply the terms with the same base by adding their exponents

21 w^{5 + 1}

Add the numbers

21 w^{6}

21 w^{6} - 15 = 0

Move the constant to the right-hand side and change its sign

21 w^{6} = 0 + 15

Removing 0 doesn't change the value,so remove it from the expression

21 w^{6} = 15

Divide both sides

\frac{21 w ^{6}}{21} = \frac{15}{21}

Divide the numbers

w^{6} = \frac{15}{21}

Cancel out the common factor 3

w^{6} = \frac{5}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

w = \pm 6 \frac{5}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{5}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 5}{6 7}

Multiply by the Conjugate

\frac{6 5 \times 6 7 ^{5}}{6 7 \times 6 7 ^{5}}

Simplify

\frac{6 5 \times 6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 616807

The product of roots with the same index is equal to the root of the product

6 5 \times 16807

Calculate the product

684035

\frac{6 84035}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

The product of roots with the same index is equal to the root of the product

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 84035}{7}

w = \pm \frac{6 84035}{7}

Separate the equation into 2 possible cases

w = \frac{6 84035}{7} w = - \frac{6 84035}{7}

Solution

w_{1} = - \frac{6 84035}{7}, w_{2} = \frac{6 84035}{7}

Alternative Form

w_{1} \approx - 0.945465, w_{2} \approx 0.945465

Show Solution