Basic Math Examples

${(\frac{- 3 b^{4}}{7})}^{4} \cdot {(\frac{- 3 b^{4}}{7})}^{- 6}$

Step 1

Multiply ${(\frac{- 3 b^{4}}{7})}^{4}$ by ${(\frac{- 3 b^{4}}{7})}^{- 6}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{- 3 b^{4}}{7})}^{4 - 6}$

Step 1.2

Subtract $6$ from $4$ .

${(\frac{- 3 b^{4}}{7})}^{- 2}$

Step 2

Move the negative in front of the fraction.

${(- \frac{3 b^{4}}{7})}^{- 2}$

Step 3

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

${(- \frac{7}{3 b^{4}})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $- \frac{7}{3 b^{4}}$ .

${(- 1)}^{2} {(\frac{7}{3 b^{4}})}^{2}$

Step 4.2

Apply the product rule to $\frac{7}{3 b^{4}}$ .

${(- 1)}^{2} \frac{7^{2}}{{(3 b^{4})}^{2}}$

Step 4.3

Apply the product rule to $3 b^{4}$ .

${(- 1)}^{2} \frac{7^{2}}{3^{2} {(b^{4})}^{2}}$

Step 5

Simplify the expression.

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Step 5.1

Raise $- 1$ to the power of $2$ .

$1 \frac{7^{2}}{3^{2} {(b^{4})}^{2}}$

Step 5.2

Multiply $\frac{7^{2}}{3^{2} {(b^{4})}^{2}}$ by $1$ .

$\frac{7^{2}}{3^{2} {(b^{4})}^{2}}$

Step 5.3

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

$\frac{49}{3^{2} {(b^{4})}^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{49}{9 {(b^{4})}^{2}}$

Step 6.2

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

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Step 6.2.1

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

$\frac{49}{9 b^{4 \cdot 2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{49}{9 b^{8}}$