Simplify (2t^-3)^3(0.4r)^2

${(2 t^{- 3})}^{3} {(0.4 r)}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(2 \frac{1}{t^{3}})}^{3} {(0.4 r)}^{2}$

Step 2

Combine $2$ and $\frac{1}{t^{3}}$ .

${(\frac{2}{t^{3}})}^{3} {(0.4 r)}^{2}$

Step 3

Simplify the expression.

Apply the product rule to $\frac{2}{t^{3}}$ .

$\frac{2^{3}}{{(t^{3})}^{3}} {(0.4 r)}^{2}$

Raise $2$ to the power of $3$ .

$\frac{8}{{(t^{3})}^{3}} {(0.4 r)}^{2}$

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

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

$\frac{8}{t^{3 \cdot 3}} {(0.4 r)}^{2}$

Multiply $3$ by $3$ .

$\frac{8}{t^{9}} {(0.4 r)}^{2}$

Apply the product rule to $0.4 r$ .

$\frac{8}{t^{9}} ({0.4}^{2} r^{2})$

Rewrite using the commutative property of multiplication.

${0.4}^{2} \frac{8}{t^{9}} r^{2}$

Raise $0.4$ to the power of $2$ .

$0.16 \frac{8}{t^{9}} r^{2}$

Step 4

Multiply $0.16 \frac{8}{t^{9}}$ .

Combine $0.16$ and $\frac{8}{t^{9}}$ .

$\frac{0.16 \cdot 8}{t^{9}} r^{2}$

Multiply $0.16$ by $8$ .

$\frac{1.28}{t^{9}} r^{2}$

Step 5

Combine $\frac{1.28}{t^{9}}$ and $r^{2}$ .

$\frac{1.28 r^{2}}{t^{9}}$