Basic Math Examples

${(y^{- 7} z^{4})}^{- 7}$

Step 1

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

${(\frac{1}{y^{7}} z^{4})}^{- 7}$

Step 2

Combine $\frac{1}{y^{7}}$ and $z^{4}$ .

${(\frac{z^{4}}{y^{7}})}^{- 7}$

Step 3

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

${(\frac{y^{7}}{z^{4}})}^{7}$

Step 4

Apply the product rule to $\frac{y^{7}}{z^{4}}$ .

$\frac{{(y^{7})}^{7}}{{(z^{4})}^{7}}$

Step 5

Multiply the exponents in ${(y^{7})}^{7}$ .

Tap for more steps...

Step 5.1

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

$\frac{y^{7 \cdot 7}}{{(z^{4})}^{7}}$

Step 5.2

Multiply $7$ by $7$ .

$\frac{y^{49}}{{(z^{4})}^{7}}$

Step 6

Multiply the exponents in ${(z^{4})}^{7}$ .

Tap for more steps...

Step 6.1

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

$\frac{y^{49}}{z^{4 \cdot 7}}$

Step 6.2

Multiply $4$ by $7$ .

$\frac{y^{49}}{z^{28}}$