Solve (((a)^(2)b(a)^(3))/((a)^(4)(b)^(4)))^(3) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$${ \left( \frac{ { a }^{ 2 } b { a }^{ 3 } }{ { a }^{ 4 } { b }^{ 4 } } \right) }^{ 3 }$$

Evaluate

$\frac{a^{3}}{b^{9}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $2$ and $3$ to get $5$.

$$\left(\frac{a^{5}b}{a^{4}b^{4}}\right)^{3}$$

Cancel out $ba^{4}$ in both numerator and denominator.

$$\left(\frac{a}{b^{3}}\right)^{3}$$

To raise $\frac{a}{b^{3}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{3}}{\left(b^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{a^{3}}{b^{9}}$$

Expand

$\frac{a^{3}}{b^{9}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $2$ and $3$ to get $5$.

$$\left(\frac{a^{5}b}{a^{4}b^{4}}\right)^{3}$$

Cancel out $ba^{4}$ in both numerator and denominator.

$$\left(\frac{a}{b^{3}}\right)^{3}$$

To raise $\frac{a}{b^{3}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{3}}{\left(b^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{a^{3}}{b^{9}}$$