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Popular >

simplify (27^{p-1}*9^{3-p})^2

Solution

simplify

(2 7^{p - 1} \cdot 9^{3 - p})^{2}

Solution

9^{p + 3}

Solution steps

(2 7^{p - 1} \cdot 9^{3 - p})^{2}

Simplify

2 7^{p - 1} \cdot 9^{3 - p} : 3^{3 (p - 1) + 2 (- p + 3)}

= (3^{3 (p - 1) + 2 (3 - p)})^{2}

3^{3 (p - 1) + 2 (3 - p)} = 3^{p + 3}

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

Apply exponent rule:

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

= 3^{(p + 3) \cdot 2}

Apply exponent rule:

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

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

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

3^{2} = 9

= 9^{(p + 3)}

Remove parentheses:

(a) = a

= 9^{p + 3}

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Frequently Asked Questions (FAQ)

What is (27^{p-1}*9^{3-p})^2 ?
The solution to (27^{p-1}*9^{3-p})^2 is 9^{p+3}