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Popular >

simplify 8^{n+2}*12^{n-3}

Solution

simplify

8^{n + 2} \cdot 1 2^{n - 3}

Solution

3 2^{n} \cdot 3^{n - 3}

Solution steps

8^{n + 2} \cdot 1 2^{n - 3}

Factor integer

8 = 2^{3}

= (2^{3})^{n + 2} \cdot 1 2^{n - 3}

Apply exponent rule:

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

(2^{3})^{n + 2} = 2^{3 (n + 2)}

= 2^{3 (n + 2)} \cdot 1 2^{n - 3}

Factor integer

12 = 2^{2} \cdot 3

= 2^{3 (n + 2)} (2^{2} \cdot 3)^{n - 3}

Apply exponent rule:

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

(2^{2} \cdot 3)^{n - 3} = (2^{2})^{n - 3} \cdot 3^{n - 3}

= 2^{3 (n + 2)} (2^{2})^{n - 3} \cdot 3^{n - 3}

Apply exponent rule:

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

(2^{2})^{n - 3} = 2^{2 (n - 3)}

= 2^{3 (n + 2)} \cdot 2^{2 (n - 3)} \cdot 3^{n - 3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{3 (n + 2)} \cdot 2^{2 (n - 3)} = 2^{3 (n + 2) + 2 (n - 3)}

= 2^{3 (n + 2) + 2 (n - 3)} \cdot 3^{n - 3}

2^{3 (n + 2) + 2 (n - 3)} = 2^{5 n}

= 2^{5 n} \cdot 3^{n - 3}

2^{5 n} = 3 2^{n}

= 3 2^{n} \cdot 3^{n - 3}

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Frequently Asked Questions (FAQ)

What is 8^{n+2}*12^{n-3} ?
The solution to 8^{n+2}*12^{n-3} is 32^n*3^{n-3}