Solve (4g^28g^6)-(g 1)

Question

Simplify the expression

32 g^{8} - g

Evaluate

(4 g^{2} \times 8 g^{6}) - (g \times 1)

Multiply

More Steps

Multiply the terms

4 g^{2} \times 8 g^{6}

Multiply the terms

32 g^{2} \times g^{6}

Multiply the terms with the same base by adding their exponents

32 g^{2 + 6}

Add the numbers

32 g^{8}

32 g^{8} - (g \times 1)

Solution

32 g^{8} - g

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Factor the expression

g (32 g^{7} - 1)

Evaluate

(4 g^{2} \times 8 g^{6}) - (g \times 1)

Multiply

More Steps

Multiply the terms

4 g^{2} \times 8 g^{6}

Multiply the terms

32 g^{2} \times g^{6}

Multiply the terms with the same base by adding their exponents

32 g^{2 + 6}

Add the numbers

32 g^{8}

32 g^{8} - (g \times 1)

Any expression multiplied by 1 remains the same

32 g^{8} - g

Rewrite the expression

g \times 32 g^{7} - g

Solution

g (32 g^{7} - 1)

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Find the roots

g_{1} = 0, g_{2} = \frac{7 4}{2}

Alternative Form

g_{1} = 0, g_{2} \approx 0.609507

Evaluate

(4 g^{2} \times 8 g^{6}) - (g \times 1)

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

(4 g^{2} \times 8 g^{6}) - (g \times 1) = 0

Multiply

More Steps

Multiply the terms

4 g^{2} \times 8 g^{6}

Multiply the terms

32 g^{2} \times g^{6}

Multiply the terms with the same base by adding their exponents

32 g^{2 + 6}

Add the numbers

32 g^{8}

32 g^{8} - (g \times 1) = 0

Any expression multiplied by 1 remains the same

32 g^{8} - g = 0

Factor the expression

g (32 g^{7} - 1) = 0

Separate the equation into 2 possible cases

g = 0 32 g^{7} - 1 = 0

Solve the equation

More Steps

Evaluate

32 g^{7} - 1 = 0

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

32 g^{7} = 0 + 1

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

32 g^{7} = 1

Divide both sides

\frac{32 g ^{7}}{32} = \frac{1}{32}

Divide the numbers

g^{7} = \frac{1}{32}

Take the 7 -th root on both sides of the equation

7 g^{7} = 7 \frac{1}{32}

Calculate

g = 7 \frac{1}{32}

Simplify the root

More Steps

Evaluate

7 \frac{1}{32}

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

\frac{7 1}{7 32}

Simplify the radical expression

\frac{1}{7 32}

Multiply by the Conjugate

\frac{7 3 2 ^{6}}{7 32 \times 7 3 2 ^{6}}

Simplify

\frac{2 ^{4} 7 4}{7 32 \times 7 3 2 ^{6}}

Multiply the numbers

\frac{2 ^{4} 7 4}{2 ^{5}}

Reduce the fraction

\frac{7 4}{2}

g = \frac{7 4}{2}

g = 0 g = \frac{7 4}{2}

Solution

g_{1} = 0, g_{2} = \frac{7 4}{2}

Alternative Form

g_{1} = 0, g_{2} \approx 0.609507

Show Solution