Indices I：練習問題

Calculate the value of \( 7^0 \times 2^3 \).

Simplify the following expression using the rules of indices:
\( \frac{(y^3)^2}{y^{-2} \times y^5} \)

Simplify the expression \( \frac{(2a^3b^{-2})^3}{4a^5b^2} \).

Evaluate \( 5^3 \times 5^0 \div 5^1 \).

Simplify the expression \( \frac{x^8}{x^{-2}} \).

Simplify the expression \( \frac{x^7 \times x^{-3}}{x^2} \).

Evaluate \( \left(\frac{1}{49}\right)^{-\frac{1}{2}} \).

Evaluate \( \frac{25^{3/2}}{100^{1/2}} \).

(a) Evaluate the following, showing your working:

(i) \( 7^0 \)
(ii) \( 2^{-3} \)

(b) Simplify the expression \( \frac{x^4 \times x^6}{x^2} \), giving your answer in index form.

Solve the equation \( 8^{2x-1} = 4^x \).