Solve [(1/2)x^3]^5(1/3x^2)^2

$$[ ( \frac { 1 } { 2 } ) x ^ { 3 } ] ^ { 5 } ( \frac { 1 } { 3 } x ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{x^{19}}{288}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{2}x^{3}\right)^{5}\times \left(\frac{1}{3}x^{2}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(\frac{1}{2}\right)^{5}\left(x^{3}\right)^{5}\times \left(\frac{1}{3}\right)^{2}\left(x^{2}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}\left(x^{3}\right)^{5}\left(x^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{3\times 5}x^{2\times 2}$$

Multiply 3 times 5.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15}x^{2\times 2}$$

Multiply 2 times 2.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15}x^{4}$$

To multiply powers of the same base, add their exponents.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15+4}$$

Add the exponents 15 and 4.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{19}$$

Raise \frac{1}{2} to the power 5.

$$\frac{1}{32}\times \left(\frac{1}{3}\right)^{2}x^{19}$$

Raise \frac{1}{3} to the power 2.

$$\frac{1}{32}\times \frac{1}{9}x^{19}$$

Multiply \frac{1}{32} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{288}x^{19}$$

Expand

$$\frac{x^{19}}{288}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{2}x^{3}\right)^{5}\times \left(\frac{1}{3}x^{2}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(\frac{1}{2}\right)^{5}\left(x^{3}\right)^{5}\times \left(\frac{1}{3}\right)^{2}\left(x^{2}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}\left(x^{3}\right)^{5}\left(x^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{3\times 5}x^{2\times 2}$$

Multiply 3 times 5.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15}x^{2\times 2}$$

Multiply 2 times 2.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15}x^{4}$$

To multiply powers of the same base, add their exponents.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{15+4}$$

Add the exponents 15 and 4.

$$\left(\frac{1}{2}\right)^{5}\times \left(\frac{1}{3}\right)^{2}x^{19}$$

Raise \frac{1}{2} to the power 5.

$$\frac{1}{32}\times \left(\frac{1}{3}\right)^{2}x^{19}$$

Raise \frac{1}{3} to the power 2.

$$\frac{1}{32}\times \frac{1}{9}x^{19}$$

Multiply \frac{1}{32} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{288}x^{19}$$