Solve (-3/5)^2*(-3/5)^3:quad(2)(a-b)

$$( - \frac { 3 } { 5 } ) ^ { 2 } \cdot ( - \frac { 3 } { 5 } ) ^ { 3 } : \quad ( 2 ) ( a - b )$$

Evaluate

$$\frac{243\left(b-a\right)}{6250}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(-\frac{3}{5}\right)^{5}}{2}\left(a-b\right)$$

Calculate -\frac{3}{5} to the power of 5 and get -\frac{243}{3125}.

$$\frac{-\frac{243}{3125}}{2}\left(a-b\right)$$

Express \frac{-\frac{243}{3125}}{2} as a single fraction.

$$\frac{-243}{3125\times 2}\left(a-b\right)$$

Multiply 3125 and 2 to get 6250.

$$\frac{-243}{6250}\left(a-b\right)$$

Fraction \frac{-243}{6250} can be rewritten as -\frac{243}{6250} by extracting the negative sign.

$$-\frac{243}{6250}\left(a-b\right)$$

Use the distributive property to multiply -\frac{243}{6250} by a-b.

$$-\frac{243}{6250}a-\frac{243}{6250}\left(-1\right)b$$

Multiply -\frac{243}{6250} and -1 to get \frac{243}{6250}.

$$-\frac{243}{6250}a+\frac{243}{6250}b$$

Expand

$$\frac{243b-243a}{6250}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(-\frac{3}{5}\right)^{5}}{2}\left(a-b\right)$$

Calculate -\frac{3}{5} to the power of 5 and get -\frac{243}{3125}.

$$\frac{-\frac{243}{3125}}{2}\left(a-b\right)$$

Express \frac{-\frac{243}{3125}}{2} as a single fraction.

$$\frac{-243}{3125\times 2}\left(a-b\right)$$

Multiply 3125 and 2 to get 6250.

$$\frac{-243}{6250}\left(a-b\right)$$

Fraction \frac{-243}{6250} can be rewritten as -\frac{243}{6250} by extracting the negative sign.

$$-\frac{243}{6250}\left(a-b\right)$$

Use the distributive property to multiply -\frac{243}{6250} by a-b.

$$-\frac{243}{6250}a-\frac{243}{6250}\left(-1\right)b$$

Multiply -\frac{243}{6250} and -1 to get \frac{243}{6250}.

$$-\frac{243}{6250}a+\frac{243}{6250}b$$