Solve (4z^4)^2/12z^7

$$\frac { ( 4 z ^ { 4 } ) ^ { 2 } } { 12 z ^ { 7 } }$$

Evaluate

$$\frac{4z}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4z^{4}\right)^{2}\times \frac{1}{12z^{7}}$$

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

$$4^{2}\left(z^{4}\right)^{2}\times \frac{1}{12}\times \frac{1}{z^{7}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{12}\left(z^{4}\right)^{2}\times \frac{1}{z^{7}}$$

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

$$4^{2}\times \frac{1}{12}z^{4\times 2}z^{7\left(-1\right)}$$

Multiply 4 times 2.

$$4^{2}\times \frac{1}{12}z^{8}z^{7\left(-1\right)}$$

Multiply 7 times -1.

$$4^{2}\times \frac{1}{12}z^{8}z^{-7}$$

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

$$4^{2}\times \frac{1}{12}z^{8-7}$$

Add the exponents 8 and -7.

$$4^{2}\times \frac{1}{12}z^{1}$$

Raise 4 to the power 2.

$$16\times \frac{1}{12}z^{1}$$

Multiply 16 times \frac{1}{12}.

$$\frac{4}{3}z^{1}$$

For any term t, t^{1}=t.

$$\frac{4}{3}z$$

Expand

$$\frac{4z}{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4z^{4}\right)^{2}\times \frac{1}{12z^{7}}$$

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

$$4^{2}\left(z^{4}\right)^{2}\times \frac{1}{12}\times \frac{1}{z^{7}}$$

Use the Commutative Property of Multiplication.

$$4^{2}\times \frac{1}{12}\left(z^{4}\right)^{2}\times \frac{1}{z^{7}}$$

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

$$4^{2}\times \frac{1}{12}z^{4\times 2}z^{7\left(-1\right)}$$

Multiply 4 times 2.

$$4^{2}\times \frac{1}{12}z^{8}z^{7\left(-1\right)}$$

Multiply 7 times -1.

$$4^{2}\times \frac{1}{12}z^{8}z^{-7}$$

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

$$4^{2}\times \frac{1}{12}z^{8-7}$$

Add the exponents 8 and -7.

$$4^{2}\times \frac{1}{12}z^{1}$$

Raise 4 to the power 2.

$$16\times \frac{1}{12}z^{1}$$

Multiply 16 times \frac{1}{12}.

$$\frac{4}{3}z^{1}$$

For any term t, t^{1}=t.

$$\frac{4}{3}z$$