Solve (a*b)^5/a*b^5

$$\frac { ( a \cdot b ) ^ { 5 } } { a \cdot b ^ { 5 } }$$

Evaluate

$$a^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{5}\times \frac{1}{a^{1}b^{5}}$$

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

$$\left(a^{1}\right)^{5}\left(b^{1}\right)^{5}\times \frac{1}{a^{1}}\times \frac{1}{b^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{5}\times \frac{1}{a^{1}}\left(b^{1}\right)^{5}\times \frac{1}{b^{5}}$$

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

$$a^{5}\times \frac{1}{a}b^{5}b^{5\left(-1\right)}$$

Multiply 5 times -1.

$$a^{5}\times \frac{1}{a}b^{5}b^{-5}$$

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

$$a^{5-1}b^{5-5}$$

Add the exponents 5 and -1.

$$a^{4}b^{5-5}$$

Add the exponents 5 and -5.

$$a^{4}b^{0}$$

For any term t except 0, t^{0}=1.

$$a^{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$a^{4}$$

Expand

$$a^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(a^{1}b^{1}\right)^{5}\times \frac{1}{a^{1}b^{5}}$$

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

$$\left(a^{1}\right)^{5}\left(b^{1}\right)^{5}\times \frac{1}{a^{1}}\times \frac{1}{b^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(a^{1}\right)^{5}\times \frac{1}{a^{1}}\left(b^{1}\right)^{5}\times \frac{1}{b^{5}}$$

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

$$a^{5}\times \frac{1}{a}b^{5}b^{5\left(-1\right)}$$

Multiply 5 times -1.

$$a^{5}\times \frac{1}{a}b^{5}b^{-5}$$

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

$$a^{5-1}b^{5-5}$$

Add the exponents 5 and -1.

$$a^{4}b^{5-5}$$

Add the exponents 5 and -5.

$$a^{4}b^{0}$$

For any term t except 0, t^{0}=1.

$$a^{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$a^{4}$$