Solve (4x^7)^3/x^-6

$$\frac { ( 4 x ^ { 7 } ) ^ { 3 } } { x ^ { - 6 } }$$

Evaluate

$$64x^{27}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{7}\right)^{3}\times \frac{1}{x^{-6}}$$

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

$$4^{3}\left(x^{7}\right)^{3}\times \frac{1}{1}\times \frac{1}{x^{-6}}$$

Use the Commutative Property of Multiplication.

$$4^{3}\times \frac{1}{1}\left(x^{7}\right)^{3}\times \frac{1}{x^{-6}}$$

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

$$4^{3}\times \frac{1}{1}x^{7\times 3}x^{-6\left(-1\right)}$$

Multiply 7 times 3.

$$4^{3}\times \frac{1}{1}x^{21}x^{-6\left(-1\right)}$$

Multiply -6 times -1.

$$4^{3}\times \frac{1}{1}x^{21}x^{6}$$

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

$$4^{3}\times \frac{1}{1}x^{21+6}$$

Add the exponents 21 and 6.

$$4^{3}\times \frac{1}{1}x^{27}$$

Raise 4 to the power 3.

$$64\times \frac{1}{1}x^{27}$$

Expand

$$64x^{27}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(4x^{7}\right)^{3}\times \frac{1}{x^{-6}}$$

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

$$4^{3}\left(x^{7}\right)^{3}\times \frac{1}{1}\times \frac{1}{x^{-6}}$$

Use the Commutative Property of Multiplication.

$$4^{3}\times \frac{1}{1}\left(x^{7}\right)^{3}\times \frac{1}{x^{-6}}$$

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

$$4^{3}\times \frac{1}{1}x^{7\times 3}x^{-6\left(-1\right)}$$

Multiply 7 times 3.

$$4^{3}\times \frac{1}{1}x^{21}x^{-6\left(-1\right)}$$

Multiply -6 times -1.

$$4^{3}\times \frac{1}{1}x^{21}x^{6}$$

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

$$4^{3}\times \frac{1}{1}x^{21+6}$$

Add the exponents 21 and 6.

$$4^{3}\times \frac{1}{1}x^{27}$$

Raise 4 to the power 3.

$$64\times \frac{1}{1}x^{27}$$