Algebra Examples

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

Step 1

Multiply the exponents in ${(4^{3})}^{- 2}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2

Multiply $3$ by $- 2$ .

$4^{- 6} \cdot {(- 8)}^{3}$

Step 2

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

$\frac{1}{4^{6}} \cdot {(- 8)}^{3}$

Step 3

Evaluate the exponents.

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Step 3.1

Raise $4$ to the power of $6$ .

$\frac{1}{4096} \cdot {(- 8)}^{3}$

Step 3.2

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

$\frac{1}{4096} \cdot - 512$

Step 4

Cancel the common factor of $512$ .

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Step 4.1

Factor $512$ out of $4096$ .

$\frac{1}{512 (8)} \cdot - 512$

Step 4.2

Factor $512$ out of $- 512$ .

$\frac{1}{512 \cdot 8} \cdot (512 \cdot - 1)$

Step 4.3

Cancel the common factor.

$\frac{1}{512 \cdot 8} \cdot (512 \cdot - 1)$

Step 4.4

Rewrite the expression.

$\frac{1}{8} \cdot - 1$

Step 5

Combine $\frac{1}{8}$ and $- 1$ .

$\frac{- 1}{8}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{8}$

Decimal Form:

$- 0.125$