Algebra Examples

${(- 4^{- 6} y^{- 6})}^{- 4}$

Step 1

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

${(- \frac{1}{4^{6}} y^{- 6})}^{- 4}$

Step 2

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

${(- \frac{1}{4096} y^{- 6})}^{- 4}$

Step 3

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

${(- \frac{1}{4096} \cdot \frac{1}{y^{6}})}^{- 4}$

Step 4

Multiply $\frac{1}{y^{6}}$ by $\frac{1}{4096}$ .

${(- \frac{1}{y^{6} \cdot 4096})}^{- 4}$

Step 5

Move $4096$ to the left of $y^{6}$ .

${(- \frac{1}{4096 \cdot y^{6}})}^{- 4}$

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- 4096 y^{6})}^{4}$

Step 7

Apply the product rule to $- 4096 y^{6}$ .

${(- 4096)}^{4} {(y^{6})}^{4}$

Step 8

Raise $- 4096$ to the power of $4$ .

$281474976710656 {(y^{6})}^{4}$

Step 9

Multiply the exponents in ${(y^{6})}^{4}$ .

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Step 9.1

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

$281474976710656 y^{6 \cdot 4}$

Step 9.2

Multiply $6$ by $4$ .

$281474976710656 y^{24}$