Simplify (4t^-8)/(-3(t^4)^5)

$\frac{4 t^{- 8}}{- 3 {(t^{4})}^{5}}$

Step 1

Move $t^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{- 3 {(t^{4})}^{5} t^{8}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(t^{4})}^{5}$ .

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

$\frac{4}{- 3 t^{4 \cdot 5} t^{8}}$

Multiply $4$ by $5$ .

$\frac{4}{- 3 t^{20} t^{8}}$

Multiply $t^{20}$ by $t^{8}$ by adding the exponents.

Move $t^{8}$ .

$\frac{4}{- 3 (t^{8} t^{20})}$

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

$\frac{4}{- 3 t^{8 + 20}}$

Add $8$ and $20$ .

$\frac{4}{- 3 t^{28}}$

Step 3

Move the negative in front of the fraction.

$- \frac{4}{3 t^{28}}$