Simplify ((t^2)^5(t^4)^2)/((t^3)^7)

$\frac{{(t^{2})}^{5} {(t^{4})}^{2}}{{(t^{3})}^{7}}$

Step 1

Simplify the numerator.

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

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

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

Multiply $2$ by $5$ .

$\frac{t^{10} {(t^{4})}^{2}}{{(t^{3})}^{7}}$

Multiply the exponents in ${(t^{4})}^{2}$ .

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

$\frac{t^{10} t^{4 \cdot 2}}{{(t^{3})}^{7}}$

Multiply $4$ by $2$ .

$\frac{t^{10} t^{8}}{{(t^{3})}^{7}}$

Step 2

Multiply the exponents in ${(t^{3})}^{7}$ .

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

$\frac{t^{10} t^{8}}{t^{3 \cdot 7}}$

Multiply $3$ by $7$ .

$\frac{t^{10} t^{8}}{t^{21}}$

Step 3

Multiply $t^{10}$ by $t^{8}$ by adding the exponents.

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

$\frac{t^{10 + 8}}{t^{21}}$

Add $10$ and $8$ .

$\frac{t^{18}}{t^{21}}$

Step 4

Cancel the common factor of $t^{18}$ and $t^{21}$ .

Multiply by $1$ .

$\frac{t^{18} \cdot 1}{t^{21}}$

Cancel the common factors.

Factor $t^{18}$ out of $t^{21}$ .

$\frac{t^{18} \cdot 1}{t^{18} t^{3}}$

Cancel the common factor.

$\frac{t^{18} \cdot 1}{t^{18} t^{3}}$

Rewrite the expression.

$\frac{1}{t^{3}}$