Simplify (5^-2t^4u^-3)/(t^-7u^6)

$\frac{5^{- 2} t^{4} u^{- 3}}{t^{- 7} u^{6}}$

Step 1

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{t^{4} u^{- 3}}{t^{- 7} u^{6} \cdot 5^{2}}$

Step 2

Move $u^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{t^{4}}{t^{- 7} u^{6} \cdot 5^{2} u^{3}}$

Step 3

Multiply $u^{6}$ by $u^{3}$ by adding the exponents.

Move $u^{3}$ .

$\frac{t^{4}}{t^{- 7} (u^{3} u^{6}) \cdot 5^{2}}$

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

$\frac{t^{4}}{t^{- 7} u^{3 + 6} \cdot 5^{2}}$

Add $3$ and $6$ .

$\frac{t^{4}}{t^{- 7} u^{9} \cdot 5^{2}}$

Step 4

Move $t^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{t^{4} t^{7}}{u^{9} \cdot 5^{2}}$

Step 5

Multiply $t^{4}$ by $t^{7}$ by adding the exponents.

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

$\frac{t^{4 + 7}}{u^{9} \cdot 5^{2}}$

Add $4$ and $7$ .

$\frac{t^{11}}{u^{9} \cdot 5^{2}}$

Step 6

Raise $5$ to the power of $2$ .

$\frac{t^{11}}{u^{9} \cdot 25}$

Step 7

Move $25$ to the left of $u^{9}$ .

$\frac{t^{11}}{25 u^{9}}$