Algebra Examples

${(a^{- 2} \cdot 8^{7})}^{2}$

Step 1

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

${(\frac{1}{a^{2}} \cdot 8^{7})}^{2}$

Step 2

Raise $8$ to the power of $7$ .

${(\frac{1}{a^{2}} \cdot 2097152)}^{2}$

Step 3

Combine $\frac{1}{a^{2}}$ and $2097152$ .

${(\frac{2097152}{a^{2}})}^{2}$

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{2097152}{a^{2}}$ .

$\frac{2097152^{2}}{{(a^{2})}^{2}}$

Step 4.2

Raise $2097152$ to the power of $2$ .

$\frac{4398046511104}{{(a^{2})}^{2}}$

Step 4.3

Multiply the exponents in ${(a^{2})}^{2}$ .

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Step 4.3.1

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

$\frac{4398046511104}{a^{2 \cdot 2}}$

Step 4.3.2

Multiply $2$ by $2$ .

$\frac{4398046511104}{a^{4}}$