Write the Fraction in Simplest Form (-5(t^5)^2)/(-5t^-9)

$\frac{- 5 {(t^{5})}^{2}}{- 5 t^{- 9}}$

Step 1

Move $t^{- 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 5 {(t^{5})}^{2} t^{9}}{- 5}$

Step 2

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 {(t^{5})}^{2} t^{9}}{- 5}$

Divide ${(t^{5})}^{2} t^{9}$ by $1$ .

${(t^{5})}^{2} t^{9}$

Step 3

Multiply the exponents in ${(t^{5})}^{2}$ .

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

$t^{5 \cdot 2} t^{9}$

Multiply $5$ by $2$ .

$t^{10} t^{9}$

Step 4

Multiply $t^{10}$ by $t^{9}$ by adding the exponents.

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

$t^{10 + 9}$

Add $10$ and $9$ .

$t^{19}$