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Popular >

simplify [(a^2*b^3)^3]^4

Solution

simplify

[(a^{2} \cdot b^{3})^{3}]^{4}

Solution

a^{24} b^{36}

Solution steps

((a^{2} b^{3})^{3})^{4}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (a^{2} b^{3})^{3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= (a^{2} b^{3})^{12}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(a^{2} b^{3})^{12} = (a^{2})^{12} (b^{3})^{12}

= (a^{2})^{12} (b^{3})^{12}

Simplify

(a^{2})^{12} : a^{24}

= a^{24} (b^{3})^{12}

Simplify

(b^{3})^{12} : b^{36}

= a^{24} b^{36}

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Frequently Asked Questions (FAQ)

What is [(a^2*b^3)^3]^4 ?
The solution to [(a^2*b^3)^3]^4 is a^{24}b^{36}