Basic Math Examples

$a^{- 2} {(b a c^{2})}^{2}$

Step 1

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

$\frac{1}{a^{2}} {(b a c^{2})}^{2}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $b a c^{2}$ .

$\frac{1}{a^{2}} ({(b a)}^{2} {(c^{2})}^{2})$

Step 2.2

Apply the product rule to $b a$ .

$\frac{1}{a^{2}} (b^{2} a^{2} {(c^{2})}^{2})$

Step 3

Cancel the common factor of $a^{2}$ .

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Step 3.1

Factor $a^{2}$ out of $b^{2} a^{2} {(c^{2})}^{2}$ .

$\frac{1}{a^{2}} (a^{2} (b^{2} {(c^{2})}^{2}))$

Step 3.2

Cancel the common factor.

$\frac{1}{a^{2}} (a^{2} (b^{2} {(c^{2})}^{2}))$

Step 3.3

Rewrite the expression.

$b^{2} {(c^{2})}^{2}$

Step 4

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

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Step 4.1

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

$b^{2} c^{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$b^{2} c^{4}$