Algebra Examples

$\frac{{(5 a^{2} b^{3})}^{0}}{{(10 a^{3} b^{2})}^{- 1}}$

Step 1

Move ${(10 a^{3} b^{2})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(5 a^{2} b^{3})}^{0} (10 a^{3} b^{2})$

Step 2

Rewrite using the commutative property of multiplication.

$10 {(5 a^{2} b^{3})}^{0} a^{3} b^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 3.1

Apply the product rule to $5 a^{2} b^{3}$ .

$10 ({(5 a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 3.2

Apply the product rule to $5 a^{2}$ .

$10 (5^{0} {(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 4

Anything raised to $0$ is $1$ .

$10 (1 {(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 5

Multiply ${(a^{2})}^{0}$ by $1$ .

$10 ({(a^{2})}^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 6

Multiply the exponents in ${(a^{2})}^{0}$ .

Tap for more steps...

Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 (a^{2 \cdot 0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 6.2

Multiply $2$ by $0$ .

$10 (a^{0} {(b^{3})}^{0}) a^{3} b^{2}$

Step 7

Multiply $a^{0}$ by $a^{3}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $a^{3}$ .

$10 (a^{3} a^{0} {(b^{3})}^{0}) b^{2}$

Step 7.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 (a^{3 + 0} {(b^{3})}^{0}) b^{2}$

Step 7.3

Add $3$ and $0$ .

$10 (a^{3} {(b^{3})}^{0}) b^{2}$

Step 8

Simplify $10 (a^{3} {(b^{3})}^{0}) b^{2}$ .

$10 a^{3} b^{2}$