Algebra Examples

$(11 - 8^{- 3} \cdot 7^{- 2}) (- 8^{3} \cdot 7^{4})$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(11 - \frac{1}{8^{3}} \cdot 7^{- 2}) (- 8^{3} \cdot 7^{4})$

Step 1.2

Raise $8$ to the power of $3$ .

$(11 - \frac{1}{512} \cdot 7^{- 2}) (- 8^{3} \cdot 7^{4})$

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(11 - \frac{1}{512} \cdot \frac{1}{7^{2}}) (- 8^{3} \cdot 7^{4})$

Step 1.4

Raise $7$ to the power of $2$ .

$(11 - \frac{1}{512} \cdot \frac{1}{49}) (- 8^{3} \cdot 7^{4})$

Step 1.5

Multiply $- \frac{1}{512} \cdot \frac{1}{49}$ .

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Step 1.5.1

Multiply $\frac{1}{49}$ by $\frac{1}{512}$ .

$(11 - \frac{1}{49 \cdot 512}) (- 8^{3} \cdot 7^{4})$

Step 1.5.2

Multiply $49$ by $512$ .

$(11 - \frac{1}{25088}) (- 8^{3} \cdot 7^{4})$

Step 2

To write $11$ as a fraction with a common denominator, multiply by $\frac{25088}{25088}$ .

$(11 \cdot \frac{25088}{25088} - \frac{1}{25088}) (- 8^{3} \cdot 7^{4})$

Step 3

Combine $11$ and $\frac{25088}{25088}$ .

$(\frac{11 \cdot 25088}{25088} - \frac{1}{25088}) (- 8^{3} \cdot 7^{4})$

Step 4

Combine the numerators over the common denominator.

$\frac{11 \cdot 25088 - 1}{25088} (- 8^{3} \cdot 7^{4})$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $11$ by $25088$ .

$\frac{275968 - 1}{25088} (- 8^{3} \cdot 7^{4})$

Step 5.2

Subtract $1$ from $275968$ .

$\frac{275967}{25088} (- 8^{3} \cdot 7^{4})$

Step 6

Raise $8$ to the power of $3$ .

$\frac{275967}{25088} (- 1 \cdot 512 \cdot 7^{4})$

Step 7

Cancel the common factor of $512$ .

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Step 7.1

Factor $512$ out of $25088$ .

$\frac{275967}{512 (49)} (- 1 \cdot 512 \cdot 7^{4})$

Step 7.2

Factor $512$ out of $- 1 \cdot 512 \cdot 7^{4}$ .

$\frac{275967}{512 (49)} (512 (- 1 \cdot 7^{4}))$

Step 7.3

Cancel the common factor.

$\frac{275967}{512 \cdot 49} (512 (- 1 \cdot 7^{4}))$

Step 7.4

Rewrite the expression.

$\frac{275967}{49} (- 1 \cdot 7^{4})$

Step 8

Combine $\frac{275967}{49}$ and $7^{4}$ .

$- 1 \cdot \frac{275967 \cdot 7^{4}}{49}$

Step 9

Simplify the expression.

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Step 9.1

Raise $7$ to the power of $4$ .

$- 1 \cdot \frac{275967 \cdot 2401}{49}$

Step 9.2

Multiply $275967$ by $2401$ .

$- 1 \cdot \frac{662596767}{49}$

Step 9.3

Divide $662596767$ by $49$ .

$- 1 \cdot 13522383$

Step 9.4

Multiply $- 1$ by $13522383$ .

$- 13522383$