Powers and roots：練習問題

Calculate the value of \( \sqrt{144} + 4^3 \).

Evaluate \( 81^{\frac{3}{4}} \).

If \( p^{-\frac{1}{2}} = \frac{1}{4} \), find the value of \( p \).

Calculate the value of \( (3^2 - \sqrt{25}) \div 2 \).

Calculate the exact value of the following expression:
\( \sqrt[3]{216} \times 4^{-\frac{3}{2}} + \sqrt{0.25} \)

Calculate the value of $$ \sqrt[3]{125} + 4^2 $$.

Evaluate \( (64^{1/3})^2 \).

If \( 4^m = 8^{m-1} \), find the value of \( m \).

Work out the value of each of the following:

(a) $8^2$

(b) $\sqrt{121}$

(c) $3^3$

(d) $\sqrt[3]{64}$

(e) $2^4 \times 5^0$

Simplify the following expressions, giving your answers with positive indices only:

(a) $$ (3x^2y^{-3})^2 \times 2x^{-1}y^5 $$

(b) $$ \frac{10a^5b^2}{(5a^{-2}b^4)^{-1}} $$

(c) Solve for $$ n $$: $$ 27^{n-1} = 9^{2n} $$