Simplify ((t^4)/(10y^4))^-4

${(\frac{t^{4}}{10 y^{4}})}^{- 4}$

Step 1

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

${(\frac{10 y^{4}}{t^{4}})}^{4}$

Step 2

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

Apply the product rule to $\frac{10 y^{4}}{t^{4}}$ .

$\frac{{(10 y^{4})}^{4}}{{(t^{4})}^{4}}$

Apply the product rule to $10 y^{4}$ .

$\frac{10^{4} {(y^{4})}^{4}}{{(t^{4})}^{4}}$

Step 3

Simplify the numerator.

Raise $10$ to the power of $4$ .

$\frac{10000 {(y^{4})}^{4}}{{(t^{4})}^{4}}$

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

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

$\frac{10000 y^{4 \cdot 4}}{{(t^{4})}^{4}}$

Multiply $4$ by $4$ .

$\frac{10000 y^{16}}{{(t^{4})}^{4}}$

Step 4

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

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

$\frac{10000 y^{16}}{t^{4 \cdot 4}}$

Multiply $4$ by $4$ .

$\frac{10000 y^{16}}{t^{16}}$